Cosmological Data Prefer An Interacting Vacuum Energy

(From Left to Right) Najla Said, Valentina Salvatelli, Marco Bruni, David Wands.

Authors: Najla Said¹, Valentina Salvatelli^1,2, Marco Bruni³, David Wands³

Affiliation:
¹Physics Department and INFN, Universita di Roma "La Sapienza", Rome, Italy
²Aix-Marseille Universite, Centre de Physique Theorique UMR 7332, France 
³Institute of Cosmology and Gravitation, University of Portsmouth, UK.

Over recent years, a growing number of high precision observations of the primordial Universe and our local cosmic neighbourhood have established a standard cosmological model, called LCDM. In LCDM, the Universe is filled with a constant dark energy, or cosmological constant (Lambda) that is responsible for the present accelerated expansion. Besides dark energy, a similar density of cold dark matter (CDM) supports the growth of large-scale structures (galaxies and clusters of galaxies) in broad agreement with the observations.

A crucial dataset for cosmological research is the Cosmic Microwave Background (CMB). This faint thermal radiation, which fills the whole sky, is a relic of the primordial Universe; it has been fundamental in supporting the homogeneity and isotropy of the Universe and in determining its composition. At the beginning of this year the Planck satellite of the European Space Agency (ESA) released a new set of CMB observations at striking precision, tightly constraining the parameters of the standard model [1].

These primordial Universe observations can be combined with a series of local Universe observations, coming from a number of galaxy surveys (SDSS [2], WiggleZ [3] and others). With these measurements we can map the distribution of structures at different epochs and use these maps to study their evolution up until the present. In particular, spectroscopic galaxy surveys enable us to quantify the clustering of the large-scale structure by measuring the so-called Redshift-Space Distortions (RSD) [4].

Since the late 1990s, the LCDM model has provided a simple framework to consistently describe local and primordial observations, but the latest precise measurements suggest that we may need to review and possibly revise this standard model. The clustering of structures, appears to be weaker than the one inferred from CMB observations assuming the standard LCDM evolution [10]. A common extension to the LCDM model is to allow the dark energy to have a non-constant density that evolves with time, but this, on its own, does not appear to resolve the conflict between different datasets [11].

In our recent work we investigated how the growth of structure is affected by an interaction between dark energy and dark matter [5,6,7]. These two components are usually assumed to evolve independently, and indeed an interaction between the two is not favored if one looks only at CMB measurements, for which the simple LCDM model fits perfectly the observations. We used the formalism of the Interacting Vacuum models, as developed in [5].

Figure 1

Our idea was to study a time-dependent interaction, but without imposing a-priori a specific time dependence. We parametrized the interaction in a simple, linear way, and studied its value at different epochs using a binned function, as sketched in Figure 1. On the x-axis we show the redshift z (a measure of time, where z=0 is today and z>0 is the past), while on the y-axis we show the dimensionless coupling parameter q_v. The purple line represents the binned model. The datasets we used for the analysis were the current CMB measurements from Planck and the RSD measurements from a number of surveys (refer to our Letter [8] for details).

The results we found suggested that an interaction at primordial epochs is not favored, but a zero coupling at recent times is excluded at 99% confidence level.

Starting from here we determined a best-fit model in which an interaction in the dark sector began around redshift z=1 (6 billion years ago) finding that, from a Bayesian point of view, this model is favored with respect to LCDM. This best-fit model is represented with the blue line in Figure 1.

We also compared our model to a cosmology with massive neutrinos [9], which is another extension of LCDM that has been proposed to solve the tension between primordial and local observations. In this case too we found that the observational evidence favors an interaction in the dark sector.

Figure 2

In Figure 2 we show the RSD dataset used in our work. On the x-axis we show the redshift z and on the y-axis the fσ₈ value, a typical measure of the growth of structure. The grey line, representing the LCDM model, predicts a higher growth than that observed, while our late-time interaction model, the blue line, fits the data much better.

The latest observations thus not only confirm that dark matter decay into dark energy is allowed, but also suggests that this interaction is actually favored with respect to the standard LCDM model.

References:
[1] P. A. R. Ade et al., ``Planck 2013 results. XVI. Cosmological parameters'', Astronomy & Astrophysics, 571, A16 (2014). Abstract.
[2] Lauren Anderson et al., ``The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples''. arXiv:1312.4877 [astro-ph.CO] (2014).
[3] Chris Blake, Sarah Brough, Matthew Colless, Carlos Contreras, Warrick Couch, Scott Croom, Tamara Davis, Michael J. Drinkwater, Karl Forster, David Gilbank, Mike Gladders, Karl Glazebrook, Ben Jelliffe, Russell J. Jurek, I-hui Li, Barry Madore, D. Christopher Martin, Kevin Pimbblet, Gregory B. Poole, Michael Pracy, Rob Sharp, Emily Wisnioski, David Woods, Ted K. Wyder, H. K. C. Yee, "The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9", Monthly Notices of the  Royal Astronomical Society, 415, 2876 (2011). Full Article.
[4] Lado Samushia, Beth A. Reid, Martin White, Will J. Percival, Antonio J. Cuesta, Lucas Lombriser, Marc Manera, Robert C. Nichol, Donald P. Schneider, Dmitry Bizyaev, Howard Brewington, Elena Malanushenko, Viktor Malanushenko, Daniel Oravetz, Kaike Pan, Audrey Simmons, Alaina Shelden, Stephanie Snedden, Jeremy L. Tinker, Benjamin A. Weaver, Donald G. York, Gong-Bo Zhao, "The Clustering of Galaxies in the SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Testing Deviations from Lambda and General Relativity using anisotropic clustering of galaxies'', Monthly Notices of the  Royal Astronomical Society, 429, 1514 (2013). Abstract.
[5] David Wands, Josue De-Santiago, Yuting Wang, "Inhomogeneous vacuum energy", Classical and Quantum Gravity, 29, 145017 (2012). Abstract.
[6] Claudia Quercellini, Marco Bruni, Amedeo Balbi, Davide Pietrobon, "Late universe dynamics with scale-independent linear couplings in the dark sector". Physical Review D, 78, 063527 (2008). Abstract.
[7] Valentina Salvatelli, Andrea Marchini, Laura Lopez-Honorez, Olga Mena, "New constraints on Coupled Dark Energy from the Planck satellite experiment", Physical Review D, 88, 023531 (2013). Abstract.
[8] Valentina Salvatelli, Najla Said, Marco Bruni, Alessandro Melchiorri, David Wands, "Indications of a late-time interaction in the dark sector", Physical Review Letters, 113, 181301 (2014). Abstract.
[9] Richard A. Battye, Adam Moss, "Evidence for massive neutrinos from CMB and lensing observations'', Physical Review Letters, 112, 051303 (2014). Abstract.
[10] E. Macaulay, I. K. Wehus, H. K. Eriksen, "Lower growth rate from recent redshift space distortion measurements than expected from Planck". Physical Review Letters, 111, 161301 (2013). Abstract.
[11] Eduardo J. Ruiz, Dragan Huterer, "Banana Split: Testing the Dark Energy Consistency with Geometry and Growth". arXiv:1410.5832 [astro-ph.CO] (2014).

New Mass Limit for White Dwarfs: Explains Super-Chandrasekhar Type Ia Supernovae

Upasana Das (left) and Banibrata Mukhopadhyay (right)







Authors: Upasana Das and Banibrata Mukhopadhyay

Affiliation: Dept of Physics, Indian Institute of Science, Bangalore, India

Background:

Extremely luminous explosions of white dwarfs, known as type Ia supernovae [1], have always been in the prime focus of natural science. Generally, they are believed to result from the violent thermonuclear explosion of a carbon-oxygen white dwarf, when its mass approaches the famous Chandrasekhar limit of 1.44M_⊙ [2], with M_⊙ being the mass of Sun. The observed luminosity is powered by the radioactive decay of nickel, produced in the thermonuclear explosion, to cobalt and then to iron. The characteristic nature of the variation of luminosity with time of these supernovae (see Figure 1) -- along with the consistent mass of the exploding white dwarf -- allows these supernovae to be used as a ‘standard’ for measuring far away distances (standard candle) and hence in understanding the expansion history of the universe.

Figure 1: Variation of luminosity as a function of time of a type Ia supernova [image courtesy: Wikipedia]

Observation and study of this very feature of distant supernovae led to the Nobel Prize in Physics in 2011 for the discovery of the accelerated expansion of the universe [3, 2Physics report]. Also, mainly because of the discovery of the limiting mass of white dwarfs, S. Chandrasekhar was awarded the Nobel Prize in Physics in 1983.

Chandrasekhar, by means of a remarkably simple calculation, was the first to obtain the maximum mass for a (non-magnetized, non-rotating) white dwarf [2]. So far, observations seemed to abide by this limit. However, the recent discovery of several peculiar type Ia supernovae -- namely, SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg [4,5] -- provokes us to rethink the commonly accepted scenario. These supernovae are distinctly over-luminous compared to their standard counterparts, because of their higher than usual nickel mass. They also violate the ‘luminosity-stretch relation’ and exhibit a much lower velocity of the matter ejected during the explosion. However, these anomalies can be resolved, if super-Chandrasekhar white dwarfs, with masses in the range 2.1-2.8M_⊙, are assumed to be the mass of the exploding white dwarfs (progenitors of these peculiar supernovae). Nevertheless, these non-standard ‘super-Chandrasekhar supernovae’ can no longer be used as cosmic distance indicators. However, there is no estimate of an upper limit to the mass of these super-Chandrasekhar white dwarf candidates yet. Can they be arbitrarily large? Moreover, there has been no foundational level analysis performed so far, akin to that carried out by Chandrasekhar, in order to establish a super-Chandrasekhar mass white dwarf.

Our result at a glance:

We establish a new and generic mass limit for white dwarfs which is 2.58M_⊙ [6]. This is significantly different from that proposed by Chandrasekhar. Our discovery naturally explains the over-luminous, peculiar type Ia supernovae mentioned above. We arrive at this new mass limit by exploiting the effects of the magnetic field in compact objects. The motivation behind our approach lies in the discovery of several isolated magnetized white dwarfs through the Sloan Digital Sky Survey (SDSS) with surface fields 10⁵-10⁹ gauss [7,8]. Hence their expected central fields could be 2-3 orders of magnitude higher. Moreover, about 25% of accreting white dwarfs, namely cataclysmic variables (CVs), are found to have magnetic fields as high as 10⁷-10⁸ gauss [9].

Underlying theory:

We first recall the basic formation scenario of white dwarfs. In order to do so, we have to understand the properties of degenerate electrons. When different states of a particle correspond to the same energy in quantum mechanics, they are called degenerate states. Moreover, Pauli’s exclusion principle prohibits any two identical fermions (in the present context: electrons) to occupy the same quantum state. Now, when a normal star of mass less than or of the order of 5M_ʘ exhausts its nuclear fuel [10], it undergoes a collapse leading to a small volume consisting of a lot of electrons. Being in a small volume, many such electrons tend to occupy the same energy states, and hence they become degenerate, since the energy of a particle depends on its momentum which is determined by the total volume of the system. Hence, once all the energy levels up to the Fermi level, which is the maximum allowed energy of a fermion, are filled by the electrons, there is no available space for the remaining electrons in a small volume of the collapsing star. This expels the electrons to move out leading to an outward pressure. If the force due to the outward pressure is able to balance the inward gravitational force, then the collapse halts, forming the compact star white dwarf.

Figure 2: Landau quantization in presence of magnetic field B. [image courtesy: Warwick University, UK ]

For the current purpose, we have to also recall the properties of degenerate, relativistic electrons under the influence of a strong magnetic field, neglecting any form of interactions. The energy states of a free electron in a magnetic field are quantized into what is known as Landau orbitals [11]. Figure 2 shows that how the continuous energy levels split into discrete Landau levels with the increase of magnetic field in the direction perpendicular to the motion of the electron. Larger the magnetic field, smaller is the number of Landau levels occupied. Recent works [12-14] establish that Landau quantization due to a strong magnetic field modifies the equation of state (EoS), which relates the pressure (P) with density (ρ), of the electron degenerate gas. This should influence significantly the mass and radius of the underlying white dwarf (and hence the mass-radius relation). The main aim here is to obtain the maximum possible mass of such a white dwarf (which is magnetized), and therefore a (new) mass limit. Hence we look for the regime of high density of electron degenerate gas and the corresponding EoS, which further corresponds to the high Fermi energy (E_F) of the system. This is because the highest density corresponds to the lowest volume and hence, lowest radius, which further corresponds to the limiting mass [2]. Note that the maximum Fermi energy (E_Fmax) corresponds to the maximum central density of the star. Consequently, conservation of magnetic flux (technically speaking flux freezing theorem, which is generally applicable for a compact star) argues for the maximum possible field of the system, which implies that only the ground Landau level will be occupied by the electrons.

Generally the EoS can be recast in the polytropic form of P=Kρ^Γ, when K is a constant and Γ (=1+1/n) is the polytropic index. At the highest density regime (which also corresponds to the highest magnetic field regime), Γ=2. Now combining the above EoS with the condition of magnetostatic equilibrium (when net outward force is balanced by the inward force), we obtain the mass and radius of the white dwarf to scale with its central density (ρ_c) as M ∝ K^(3/2) ρ_c^(3-n)/2n and R ∝ K^(1/2) ρ_c^(1-n)/2n respectively [6]. For Γ = 2, which corresponds to the case of limiting mass, K ∝ ρ_c^(-2/3) and hence M becomes independent of ρ_c and R becomes zero. Substituting the proportionality constants, for Γ = 2 we obtain exactly [6]:

where h is the Planck’s constant, c the speed of light, G Newton’s gravitation constant, μ_e the mean molecular weight per electron and m_H the mass of hydrogen atom. For μ_e=2, which is the case for a carbon-oxygen white dwarf, M≈2.58M_⊙. To compare with Chandrasekhar’s result [2], we recall the limiting mass obtained by him as

which for μ_e =2 is 1.44M_⊙.

Figure 3: Mass-radius relation of a white dwarf. Solid line – Chandrasekhar’s relation; dashed line – our relation.

For a better reference, we include a comparison between the mass-radius relation of the white dwarf obtained by Chandrasekhar and that obtained by us in Figure 3.

Justification of high magnetic field and its effect to hold more mass:

The presence of magnetic field in a white dwarf creates an additional outward pressure apart from that due to degenerate electrons, which is however modified in presence of a strong field in it. On the other hand, the inward (gravitational) force is proportional to the mass of the white dwarf. Hence, when the star is magnetized, a larger outward force can balance a larger inward force, allowing it to have more mass.

However, the effect of Landau quantization becomes significant only at a high field B ≥ B_c = 4.414×10¹³ gauss. How can we justify such a high field in a white dwarf? Let us consider the commonly observed phenomenon of a magnetized white dwarf attracting mass from its companion star (called accretion). Now the surface field of an accreting white dwarf, as observed, could be 10⁹ gauss (≪ B_c) [7]. Its central field, however, can be several orders of magnitude higher ∼ 10¹² gauss, which is also less than B_c. Naturally, such a magnetized CV, still follows the mass-radius relation obtained by Chandrasekhar. However, in contrast with Chandrasekhar’s work (which did not include a magnetic field in the calculations), we obtain that, a nonzero initial field in the white dwarf, however ineffective for rendering Landau quantization effects, proves to be crucial in supporting the additional mass accumulated due to accretion.

As an above-mentioned magnetized white dwarf first gains mass due to accretion, its total mass increases which in turn increases the gravitational power and hence the white dwarf contracts in size due to the increased gravitational pull. However, the total magnetic flux in a white dwarf is understood to be conserved, which is magnetic field times the square of its radius. Therefore, if the white dwarf shrinks, its radius decreases and hence magnetic field increases. This in turn increases the outward force balancing the increased inward gravitational force (due to increase of its mass), which leads to a quasi-equilibrium situation. As the accretion is a continuous process, above process of shrinking the white dwarf, increasing the magnetic field and holding more mass, goes in a cycle. This continues until the gain of mass becomes so great that total outward pressure is unable to support the gravitational attraction. This finally leads to a supernova explosion, which we observe as a peculiar, over-luminous type Ia supernova, in contrast to their normal counter parts.

Punch lines:

More than 80 years after the proposal of Chandrasekhar mass limit, this new limit perhaps heralds the onset of a paradigm shift. This discovery has several consequences as briefly described below.

The masses of white dwarfs are measured from their luminosities assuming Chandrasekhar's mass-radius relation, as of now. These results may have to be re-examined based on the new mass-radius relation, at least for some peculiar objects (e.g. over-luminous type Ia supernovae). Further, some peculiar known objects, like magnetars (highly magnetized compact objects, supposedly neutron stars, as of now) should be examined based on the above considerations, which could actually be super-Chandrasekhar white dwarfs.

This new mass limit may also lead to establishing the underlying peculiar supernovae as a new standard candle for cosmic distance measurement. Hence, in order to correctly interpret the expansion history of the universe (and then dark energy), one might need to carefully sample the observed data from the supernovae explosions, especially if the peculiar type Ia supernovae are eventually found to be enormous in number. However, it is probably too early to comment whether our discovery has any direct implication on the current dark energy scenario, which is based on the observation of ordinary type Ia supernovae.

References:
[1] D. Andrew Howell, “Type Ia supernovae as stellar endpoints and cosmological tools”, Nature Communications, 2, 350 (2011). Abstract.
[2] S. Chandrasekhar, “The highly collapsed configurations of a stellar mass (Second Paper)”, Monthly Notices of the Royal Astronomical Society, 95, 207 (1935). Article.
[3] S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, and The Supernova Cosmology Project, “Measurements of Omega and Lambda from 42 high-redshift supernovae”, The Astrophysical Journal, 517, 565 (1999). Article.
[4] D. Andrew Howell, Mark Sullivan, Peter E. Nugent, Richard S. Ellis, Alexander J. Conley, Damien Le Borgne, Raymond G. Carlberg, Julien Guy, David Balam, Stephane Basa, Dominique Fouchez, Isobel M. Hook, Eric Y. Hsiao, James D. Neill, Reynald Pain, Kathryn M. Perrett and Christopher J. Pritchet, “The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star”, Nature, 443, 308 (2006). Abstract.
[5] R. A. Scalzo, G. Aldering, P. Antilogus, C. Aragon, S. Bailey, C. Baltay, S. Bongard, C. Buton, M. Childress, N. Chotard, Y. Copin, H. K. Fakhouri, A. Gal-Yam, E. Gangler, S. Hoyer, M. Kasliwal, S. Loken, P. Nugent, R. Pain, E. Pécontal, R. Pereira, S. Perlmutter, D. Rabinowitz, A. Rau, G. Rigaudier, K. Runge, G. Smadja, C. Tao, R. C. Thomas, B. Weaver, and C. Wu, “Nearby supernova factory observations of SN2007if: First total mass measurement of a super-Chandrasekhar-mass progenitor”, The Astrophysical Journal, 713, 1073 (2010). Article.
[6] Upasana Das & Banibrata Mukhopadhyay, “New mass limit for white dwarfs: Super-Chandrasekhar type Ia supernova as a new standard candle”, Physical Review Letters, 110, 071102 (2013). Abstract.
[7] Gary D. Schmidt, Hugh C. Harris, James Liebert, Daniel J. Eisenstein, Scott F. Anderson, J. Brinkmann, Patrick B. Hall, Michael Harvanek, Suzanne Hawley, S. J. Kleinman, Gillian R. Knapp, Jurek Krzesinski, Don Q. Lamb, Dan Long, Jeffrey A. Munn, Eric H. Neilsen, Peter R. Newman, Atsuko Nitta, David J. Schlegel, Donald P. Schneider, Nicole M. Silvestri, J. Allyn Smith, Stephanie A. Snedden, Paula Szkody, and Dan Vanden Berk, “Magnetic white dwarfs from the Sloan Digital Sky Survey: The first data release”, The Astrophysical Journal, 595, 1101 (2003). Article.
[8] Karen M. Vanlandingham, Gary D. Schmidt, Daniel J. Eisenstein, Hugh C. Harris, Scott F. Anderson, Patrick B. Hall, James Liebert, Donald P. Schneider, Nicole M. Silvestri, Gregory S. Stinson, and Michael A. Wolfe, “Magnetic white dwarfs from the SDSS. II. The second and third data releases”, The Astronomical Journal, 130, 734 (2005). Article.
[9] D. T. Wickramasinghe and Lilia Ferrario, “Magnetism in isolated and binary white dwarfs”, Publications of the Astronomical Society of the Pacific, 112, 873 (2000). Article.
[10] S.L. Shapiro and S.A. Teukolsky, “Black holes, White dwarfs and Neutron stars: The physics of compact objects” (John Wiley & Sons Inc, 1983).
[11] Dong Lai and Stuart L. Shapiro, “Cold equation of state in a strong magnetic field – Effect of inverse beta-decay”, The Astrophysical Journal, 383, 745 (1991). Abstract.
[12] Upasana Das and Banibrata Mukhopadhyay, “Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf”, Physical Review D, 86, 042001 (2012). Abstract.
[13] Upasana Das and Banibrata Mukhopadhyay, “Violation of Chandrasekhar mass limit: The exciting potential of strongly magnetized white dwarfs”, Int. J. Mod. Phys. D, 21, 1242001 (2012). Abstract.
[14] Aritra Kundu and Banibrata Mukhopadhyay, “Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view”, Modern Physics Letters A, 27, 1250084 (2012). Abstract.

Building A Precision Model of the Universe from the Biggest Color 3-D Map

Shirley Ho

Since 2000, the three Sloan Digital Sky Surveys (SDSS I, II, III) have surveyed well over a quarter of the night sky and produced the biggest color map of the universe in three dimensions ever. Now scientists at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) and their SDSS colleagues, working with DOE’s National Energy Research Scientific Computing Center (NERSC) based at Berkeley Lab, have used this visual information for the most accurate calculation yet of how matter clumps together – from a time when the universe was only half its present age until now.

“The way galaxies cluster together over vast expanses of the sky tells us how both ordinary visible matter and underlying invisible dark matter are distributed, across space and back in time,” says Shirley Ho, an astrophysicist at Berkeley Lab and Carnegie Mellon University, who led the work. “The distribution gives us cosmic rulers to measure how the universe has expanded, and a basis for calculating what’s in it: how much dark matter, how much dark energy, even the mass of the hard-to-see neutrinos it contains. What’s left over is the ordinary matter and energy we’re familiar with.”

The Sloan Digital Sky Survey III surveyed 14,000 square degrees of the sky, more than a third of its total area, and delivered over a trillion pixels of imaging data. This image shows over a million luminous galaxies at redshifts indicating times when the universe was between seven and eleven billion years old, from which the sample in the current studies was selected. Click on image for best resolution. To watch animated visualizations of the luminous galaxies in the SDSS-III dataset, click here.[Credit: David Kirkby of the University of California at Irvine and the SDSS collaboration]

For the present study Ho and her colleagues first selected 900,000 luminous galaxies from among over 1.5 million such galaxies gathered by the Baryon Oscillation Spectrographic Survey, or BOSS, the largest component of the still-ongoing SDSS III. Most of these are ancient red galaxies, which contain only red stars because all their faster-burning stars are long gone, and which are exceptionally bright and visible at great distances. The galaxies chosen for this study populate the largest volume of space ever used for galaxy clustering measurements. Their brightness was measured in five different colors, allowing the redshift of each to be estimated.

“By covering such a large area of sky and working at such large distances, these measurements are able to probe the clustering of galaxies on incredibly vast scales, giving us unprecedented constraints on the expansion history, contents, and evolution of the universe,” says Martin White of Berkeley Lab’s Physics Division, a professor of physics and astronomy at the University of California at Berkeley and chair of the BOSS science survey teams. “The clustering we’re now measuring on the largest scales also contains vital information about the origin of the structure we see in our maps, all the way back to the epoch of inflation, and it helps us to constrain – or rule out – models of the very early universe.”

After augmenting their study with information from other data sets, the team derived a number of such cosmological constraints, measurements of the universe’s contents based on different cosmological models. Among the results: in the most widely accepted model, the researchers found – to less than two percent uncertainty – that dark energy accounts for 73 percent of the density of the universe.

The team’s results are presented January 11 at the annual meeting of the American Astronomical Society in Austin, Texas, and have been submitted to the Astrophysical Journal. They are currently available online [1,2].

The power of the universe

“The way mass clusters on the largest scales is graphed in an angular power spectrum, which shows how matter statistically varies in density across the sky,” says Ho. “The power spectrum gives a wealth of information, much of which is yet to be exploited.” For example, information about inflation – how the universe rapidly expanded shortly after the big bang – can be derived from the power spectrum.

Closely related to the power spectrum are two “standard rulers,” which can be used to measure the history of the expansion of the universe. One ruler has only a single mark – the time when matter and radiation were exactly equal in density.

“In the very early universe, shortly after the big bang, the universe was hot and dominated by photons, the fundamental particles of radiation,” Ho explains. “But as it expanded, it began the transition to a universe dominated by matter. By about 50,000 years after the big bang, the density of matter and radiation were equal. Only when matter dominated could structure form.”

The other cosmic ruler is also big, but it has many more than one mark in the power spectrum; this ruler is called BAO, for baryon acoustic oscillations. (Here, baryon is shorthand for ordinary matter.) Baryon acoustic oscillations are relics of the sound waves that traveled through the early universe when it was a hot, liquid-like soup of matter and photons. After about 50,000 years the matter began to dominate, and by about 300,000 years after the big bang the soup was finally cool enough for matter and light to go their separate ways.

Differences in density that the sound waves had created in the hot soup, however, left their signatures as statistical variations in the distribution of light, detectable as temperature variations in the cosmic microwave background (CMB), and in the distribution of baryons. The CMB is a kind of snapshot that can still be read today, almost 14 billion years later. Baryon oscillations – variations in galactic density peaking every 450 million light-years or so – descend directly from these fluctuations in the density of the early universe.

BAO is the target of the Baryon Oscillation Spectroscopic Survey. By the time it’s completed, BOSS will have measured the individual spectra of 1.5 million galaxies, a highly precise way of measuring their redshifts. The first BOSS spectroscopic results are expected to be announced early in 2012.

Meanwhile the photometric study by Ho and her colleagues deliberately uses many of the same luminous galaxies but derives redshifts from their brightnesses in different colors, extending the BAO ruler back over a previously inaccessible redshift range, from z = 0.45 to z = 0.65 (z stands for redshift).

“As an oscillatory feature in the power spectrum, not many things can corrupt or confuse BAO, which is why it is considered one of the most trustworthy ways to measure dark energy,” says Hee-Jong Seo of the Berkeley Center for Cosmological Physics at Berkeley Lab and the UC Berkeley Department of Physics, who led BAO measurement for the project. “We call BAO a standard ruler for a good reason. As dark energy stretches the universe against the gravity of dark matter, more dark energy places galaxies at a larger distance from us, and the BAO imprinted in their distribution looks smaller. As a standard ruler the true size of BAO is fixed, however. Thus the apparent size of BAO gives us an estimate of the cosmological distance to our target galaxies – which in turn depends on the properties of dark energy.”

Says Ho, “Our study has produced the most precise photometric measurement of BAO. Using data from the newly accessible redshift range, we have traced these wiggles back to when the universe was about half its present age, all the way back to z = 0.54.”

Seo adds, “And that’s to an accuracy within 4.5 percent.”

Reining in the systematics

“With such a large volume of the universe forming the basis of our study, precision cosmology was only possible if we could control for large-scale systematics,” says Ho. Systematic errors are those with a physical basis, including differences in the brightness of the sky, or stars that mimic the colors of distant galaxies, or variations in weather affecting “seeing” at the SDSS’s Sloan Telescope – a dedicated 2.5 meter telescope at the Apache Point Observatory in southern New Mexico.

After applying individual corrections to these and other systematics, the team cross-correlated the effects on the data and developed a novel procedure for deriving the best angular power-spectrum of the universe with the lowest statistical and systematic errors.

With the help of 40,000 central-processing-unit (CPU) hours at NERSC and another 20,000 CPU hours on the Riemann computer cluster operated by Berkeley Lab’s High-Performance Computing Services group, these powerful computers and algorithms enabled the team to use all the information from galactic clustering in a huge volume of sky, including the full shape of the power spectrum and, independently, BAO, to get excellent cosmological constraints. The data as well as the analysis output are stored at NERSC.

“Our dataset is purely imaging data, but our results are competitive with the latest large-scale spectroscopic surveys,” Ho says. “What we lack in redshift precision, we make up in sheer volume. This is good news for future imaging surveys like the Dark Energy Survey and the Large Synoptic Survey Telescope, suggesting they can achieve significant cosmological constraints even compared to future spectroscopy surveys.”

References:
[1] “Clustering of Sloan Digital Sky Survey III photometric luminous galaxies: The measurement, systematics, and cosmological implications,” by Shirley Ho, Antonio Cuesta, Hee-Jong Seo, Roland de Putter, Ashley J. Ross, Martin White, Nikhil Padmanabhan, Shun Saito, David J. Schlegel, Eddie Schlafly, Uroŝ Seljak, Carlos Hernández-Monteagudo, Ariel G. Sánchez, Will J. Percival, Michael Blanton, Ramin Skibba, Don Schneider, Beth Reid, Olga Mena, Matteo Viel, Daniel J. Eisenstein, Francisco Prada, Benjamin Weaver, Neta Bahcall, Dimitry Bizyaev, Howard Brewinton, Jon Brinkman, Luiz Nicolaci da Costa, John R. Gott, Elena Malanushenko, Viktor Malanushenko, Bob Nichol, Daniel Oravetz, Kaike Pan, Nathalie Palanque-Delabrouille, Nicholas P. Ross, Audrey Simmons, Fernando de Simoni, Stephanie Snedden,and Christophe Yeche (submitted to Astrophysical Journal). arXiv:1201.2137.
[2] “Acoustic scale from the angular power spectra of SDSS-III DR8 photometric luminous galaxies,” by Hee-Jong Seo, Shirley Ho, Martin White, Antonio J. Cuesta, Ashley J. Ross, Shun Saito, Beth Reid, Nikhil Padmanabhan, Will J. Percival, Roland de Putter, David J. Schlegel, Daniel J. Eisenstein, Xiaoying Xu, Donald P. Schneider, Ramin Skibba, Licia Verde, Robert C. Nichol, Dmitry Bizyaev, Howard Brewington, J. Brinkmann, Luiz Alberto Nicolai da Costa, J. Richard Gott III, Elena Malanushenko, Viktor Malanushenko, Dan Oravetz, Nathalie Palanque-Delabrouille, Kaike Pan, Francisco Prada, Nicholas P. Ross, Audrey Simmons, Fernando Simoni, Alaina Shelden, Stephanie Snedden, and Idit Zehavi (submitted to Astrophysical Journal). arXiv:1201.2172 .

[This report is written by Paul Preuss of Lawrence Berkeley National Laboratory]

Physics Nobel Prize 2011: Accelerating Expansion of the Universe

[L to R] Saul Perlmutter, Brian P. Schmidt, Adam G. Riess

The Nobel Prize in Physics 2011 was awarded "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae" with one half to Saul Perlmutter and the other half jointly to Brian P. Schmidt and Adam G. Riess.

Here are the contact information and links to their homepages and institutes:

Saul Perlmutter, The Supernova Cosmology Project, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA

Brian P. Schmidt, The High-z Supernova Search Team, Australian National University, Weston Creek, Australia

Adam G. Riess, The High-z Supernova Search Team, Johns Hopkins University and Space Telescope Science Institute, Baltimore, MD, USA

Past 2Physics article on the work of Saul Perlmutter:
April 25, 2010: "Searching Dark Energy with Supernova Dataset"

"Some say the world will end in fire, some say in ice..."
(Robert Frost, Fire and Ice, 1920)

What will be the final destiny of the Universe? Probably it will end in ice, if we are to believe this year's Nobel Laureates in Physics. They have studied several dozen exploding stars, called supernovae, and discovered that the Universe is expanding at an ever-accelerating rate. The discovery came as a complete surprise even to the Laureates themselves.

In 1998, cosmology was shaken at its foundations as two research teams presented their findings. Headed by Saul Perlmutter, one of the teams had set to work in 1988. Brian Schmidt headed another team, launched at the end of 1994, where Adam Riess was to play a crucial role.

The research teams raced to map the Universe by locating the most distant supernovae. More sophisticated telescopes on the ground and in space, as well as more powerful computers and new digital imaging sensors (CCD, Nobel Prize in Physics in 2009), opened the possibility in the 1990s to add more pieces to the cosmological puzzle.

The teams used a particular kind of supernova, called type Ia supernova. It is an explosion of an old compact star that is as heavy as the Sun but as small as the Earth. A single such supernova can emit as much light as a whole galaxy. All in all, the two research teams found over 50 distant supernovae whose light was weaker than expected - this was a sign that the expansion of the Universe was accelerating. The potential pitfalls had been numerous, and the scientists found reassurance in the fact that both groups had reached the same astonishing conclusion.

For almost a century, the Universe has been known to be expanding as a consequence of the Big Bang about 14 billion years ago. However, the discovery that this expansion is accelerating is astounding. If the expansion will continue to speed up the Universe will end in ice.

The acceleration is thought to be driven by dark energy, but what that dark energy is remains an enigma - perhaps the greatest in physics today. What is known is that dark energy constitutes about three quarters of the Universe. Therefore the findings of the 2011 Nobel Laureates in Physics have helped to unveil a Universe that to a large extent is unknown to science. And everything is possible again.

Largest 3-D Map of the Distant Universe Created by Using Light from 14000 Quasars

Anže Slosar [photo courtesy: Skorpinski/Berkeley Center for Cosmological Physics]

In a meeting of the American Physical Society in Anaheim, California on May 1, Anže Slosar, a physicist at the U.S. Department of Energy's Brookhaven National Laboratory, presented the largest ever three-dimensional map of the distant universe created by using the light of 14,000 quasars to illuminate ghostly clouds of intergalactic hydrogen.

The map was created by a team of scientists from the Sloan Digital Sky Survey (SDSS-III) by using a 2.5-meter telescope with a wide field of view. This will provide an unprecedented view of what the universe looked like 11 billion years ago and the role of dark energy in accelerating the expansion of the universe during that era. The findings are described in an article posted online on the arXiv astrophysics preprint server [1].

The new technique used by Slosar and his colleagues turns the standard approach of astronomy on its head. "Usually we make our maps of the universe by looking at galaxies, which emit light," Slosar explained. "But here, we are looking at intergalactic hydrogen gas, which blocks light. It's like looking at the moon through clouds — you can see the shapes of the clouds by the moonlight that they block."

Instead of the moon, the SDSS team observed quasars, brilliantly luminous beacons powered by giant black holes. Quasars are bright enough to be seen billions of light years from Earth, but at these distances they look like tiny, faint points of light. As light from a quasar travels on its long journey to Earth, it passes through clouds of intergalactic hydrogen gas that absorb light at specific wavelengths, which depend on the distances to the clouds. This patchy absorption imprints an irregular pattern on the quasar light known as the "Lyman-alpha forest."

[Click on the image to see a better resolution version] A slice through the three-dimensional map of the universe. We are looking out from the Milky Way, at the bottom tip of the wedge. Distances are labeled on the right in billions of light-years, and each section of the map is labeled on the left. The black dots going out to about 7 billion light years are nearby galaxies. The red cross-hatched region could not be observed with the SDSS telescope, but the future BigBOSS survey could observe it. The colored region shows the map of intergalactic hydrogen gas in the distant universe. Red areas have more gas; blue areas have less gas. This figure is a slice through the full three-dimensional map. [Image credit: A. Slosar and the SDSS-III collaboration].

An observation of a single quasar gives a map of the hydrogen in the direction of the quasar, Slosar explained. The key to making a full, three-dimensional map is numbers. "When we use moonlight to look at clouds in the atmosphere, we only have one moon. But if we had 14,000 moons all over the sky, we could look at the light blocked by clouds in front of all of them, much like what we can see during the day. You don't just get many small pictures — you get the big picture."

The big picture shown in Slosar's map contains important clues to the history of the universe. The map shows a time 11 billion years ago, when the first galaxies were just starting to come together under the force of gravity to form the first large clusters. As the galaxies moved, the intergalacitc hydrogen moved with them. Andreu Font-Ribera, a graduate student at the Institute of Space Sciences in Barcelona, created computer models of how the gas likely moved as those clusters formed. The results of his computer models matched well with the map. "That tells us that we really do understand what we're measuring," Font-Ribera said. "With that information, we can compare the universe then to the universe now, and learn how things have changed."

[Click on the image to see a better resolution version] A zoomed-in view of the map slice shown in the previous image. Red areas have more gas; blue areas have less gas. The black scalebar in the bottom right measures one billion light years. [Image credit: A. Slosar and the SDSS-III collaboration].

The quasar observations come from the Baryon Oscillation Spectroscopic Survey (BOSS), the largest of the four surveys that make up SDSS-III. Eric Aubourg, from the University of Paris, led a team of French astronomers who visually inspected every one of the 14,000 quasars individually. "The final analysis is done by computers," Aubourg said, "but when it comes to spotting problems and finding surprises, there are still things a human can do that a computer can't."

Past 2Physics articles on BOSS:
March 28, 2010: "General Relativity Is Valid On Cosmic Scale"
October 03, 2009: "BOSS – A New Kind of Search for Dark Energy"

"BOSS is the first time anyone has used the Lyman-alpha forest to measure the three-dimensional structure of the universe," said David Schlegel, a physicist at Lawrence Berkeley National Laboratory in California and the principal investigator of BOSS. "With any new technique, people are nervous about whether you can really pull it off, but now we've shown that we can." In addition to BOSS, Schlegel noted, the new mapping technique can be applied to future, still more ambitious surveys, like its proposed successor BigBOSS.

When BOSS observations are completed in 2014, astronomers can make a map ten times larger than the one being released today, according to Patrick McDonald of Lawrence Berkeley National Laboratory and Brookhaven National Laboratory, who pioneered techniques for measuring the universe with the Lyman-alpha forest and helped design the BOSS quasar survey. BOSS's ultimate goal is to use subtle features in maps like Slosar's to study how the expansion of the universe has changed during its history. "By the time BOSS ends, we will be able to measure how fast the universe was expanding 11 billion years ago with an accuracy of a couple of percent. Considering that no one has ever measured the cosmic expansion rate so far back in time, that's a pretty astonishing prospect."

Quasar expert Patrick Petitjean of the Institut d'Astrophysique de Paris, a key member of Aubourg's quasar-inspecting team, is looking forward to the continuing flood of BOSS data. "Fourteen thousand quasars down, one hundred and forty thousand to go," he said. "If BOSS finds them, we'll be happy to look at them all, one by one. With that much data, we're bound to find things that we never expected."

Reference
[1] "The Lyman-alpha forest in three dimensions: measurements of large scale flux correlations from BOSS 1st-year data," by Anže Slosar, Andreu Font-Ribera, Matthew M. Pieri, James Rich, Jean-Marc Le Goff, Eric Aubourg, John Brinkmann, Nicolas Busca, Bill Carithers, Romain Charlassier, Marina Cortes, Rupert Croft, Kyle S. Dawson, Daniel Eisenstein, Jean-Christophe Hamilton, Shirley Ho, Khee-Gan Lee, Robert Lupton, Patrick McDonald, Bumbarija Medolin, Jordi Miralda-Escudé, Adam D. Myers, Robert C. Nichol, Nathalie Palanque-Delabrouille, Isabelle Paris, Patrick Petitjean, Yodovina Piskur, Emmanuel Rollinde, Nicholas P. Ross, David J. Schlegel, Donald P. Schneider, Erin Sheldon, Benjamin A. Weaver, David H. Weinberg, Christophe Yeche, and Don York. Available online: arXiv:1104.5244.