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1
Shanghai Astronomical Observatory, CAS, Shanghai, 200030
Our understanding of the universe has been greatly advanced over the last two decades and a standard cosmology paradigm is now well established. Standard cosmology is based upon the cosmological principle that our universe is statistically homogeneous and isotropic.
It is also based upon general relativity with a non-zero cosmological constant. In such a framework, our universe is composed of about 4% ordinary matter (baryonic matter), about one quarter of non-baryonic cold dark matter which virtually only interacts with baryons gravitationally, and three quarters of cosmological constant (or dark energy in general). With as minimal as six parameters (the baryon density, the cold non-baryonic dark matter density, the present day expansion rate, the shape and the amplitude of primordial fluctuations, and the Thomson optical depth to the last scattering surface), it can amazingly explain almost every piece of cosmological observation.
An incomplete list of milestones during this revolutionary epoch of cosmology is given as follows: l 1992: The first detection of primordial fluctuations in the cosmic microwave background (CMB) by the COBE satellite. l 1998: Discovery of late-time cosmic acceleration, inferred from the distance-redshift relation measured through distant type Ia supernovae.
l 2000: Detection of tiny distortion in distant galaxy images induced by weak gravitational lensing; Detection of distortions in galaxy clustering pattern by the large scale peculiar velocity; and Precision measurement of 2D and 3D galaxy clustering using 2dF and SDSS galaxies around this period. l 2003: Precision measurement of CMB fluctuations by WMAP; Detection of decay of the large scale gravitational potential through the integrated Sachs-Wolfe effect.
l 2005: Detection of baryon acoustic oscillation in galaxy clustering, which is essentially the frozen sound wave in baryon fluid of the early universe. l 2008
-
2009: Discoveries of previously unknown galaxy clusters through their imprints in the CMB sky (the
ZHANG Pengjie is a professor at the CAS Shanghai Astronomical Observatory. His interests of research focus on the Sunyaev Zel'dovich effect, weak gravitational lensing, cosmological tests of general relativity and other issues on theoretical cosmology. After obtaining his B.S. from the Peking University in 1997 and Ph.D from the University of Toronto in 2003, he worked as a postdoctoral research associate at the Fermilab from 2003 to 2005. He was recruited by the
“One-hundred Talent” Program of CAS in 2005 and won the National Science Foundation for
Distinguished Young Scholars of China in 2010.
1 Correspondence and requests for materials should be addressed to pjzhang@shao.ac.cn.
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thermal Sunyaev Zel’dovich (SZ) effect) and detection of the diffuse SZ effect in blank sky. l 2011: Detection of the lensing distortion on CMB and confirmation of cosmic acceleration from CMB observation alone.
These great discoveries and precision measurements, on the one hand, led to the establishment of standard cosmology; on the other, they have provided invaluable opportunities to scrutinize fundamental cosmological physics and to test foundations of modern cosmology. Again an incomplete list follows: What is the origin mechanism of the observable universe? Is dark energy the cosmological constant or dynamical? Is general relativity valid at cosmological scales? Is the universe homogeneous? There are numerous works on these issues. Here I only briefly discuss the last two questions, the validity of general relativity and the Copernican principle , with introduction to our works on these topics.
One version of the Copernican principle claims that we do not reside in a special region of the universe. A stronger claim is that, statistically speaking, there is no special region in the universe. The Copernican principle has been a fundamental tenet of modern science since the 16 th century and is also a cornerstone of modern cosmology. So far the statistical homogeneity of the last scattering surface has been verified by cosmic microwave background (CMB) observations and the radial homogeneity up to the Gpc scale by galaxy surveys. However, radial homogeneity at larger scales remains unproven.
Testing the Copernican principle is of crucial importance for fundamental cosmology. If the Copernican principle is violated such that we live in or near the center of a large
(up to Gpc scale) void as described by a Lematre-Tolman-
Bondi (LTB) space-time in which the matter distribution is spherically symmetric, the apparent cosmic acceleration can be explained without cosmological constant, dark energy or modifications of general relativity. For this reason, most works on testing the Copernican principle focus on this type of non-Copernican universe. Various tests of the Copernican principle have been proposed and a large class of void models has been ruled out.
Recently we proposed a powerful single test which confirms the Copernican principle at Gpc radial scale
(Zhang and Stebbins, 2011). The key idea is that, in a non-
Copernican universe, some regions will expand faster or slower than others and as photons transit between these regions there will be a relative motion between the average matter frame and CMB. Through the inverse Compton scattering between free electrons and CMB photons, this relative motion induces a shift of the brightness temperature of CMB photons via the kinetic Sunyaev Zel’dovich (kSZ) effect. This temperature shift will be anisotropic on our sky tracing the anisotropy of the projected free electron surface density. This test of the Copernican principle has been applied to cluster kSZ observations, where the electron surface density is high.
Furthermore, the kSZ effect applies to all free electrons existing in great abundance everywhere in the universe up to the reionization epoch at redshift z>6 (and comoving distance bigger than 6 Gpc), whereas clusters are rare above z>1. It is exactly for this reason why the kSZ test from blank field
CMB anisotropy power spectrum measurements is more sensitive than that from cluster kSZ measurements. Fig. 1 shows its great discriminating power against violations of the Copernican principle. The model shown in this figure is a popular LTB model called Hubble bubble. The kSZ test robustly ruled out all Hubble bubble models larger than Gpc size, which also produce larger kSZ effects than allowed by recent measurements by SZ surveys of the Atacama
Cosmology Telescope (ACT, Dunkley et al ., 2010) and the
South Pole Telescope (SPT, Shirokoff et al ., 2010). Surviving
Hubble bubbles are too small to drive the observed “cosmic acceleration.” Hence Hubble bubble model is no longer a viable alternative to cosmic acceleration.
Fig.1 The kSZ test. Black curves have constant kSZ power spectrum. The thick one highlights the SPT 95% upper limit.
The kSZ test alone rules out large voids with low density and strongly supports the Copernican principle. The dashed and dotted contours are the 2-σ and 3-σ constraints from the UNION2 supernova data. The kSZ test robustly excludes the Hubble bubble model as a viable alternative to dark energy.
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There are many other classes of void models. Although we have not performed numerical calculation for them, our kSZ test is expected to be a generic test, and it is hard for any of these models to pass the test without extra dramatic modifications to standard cosmology, such as the adiabaticity of the universe. Hence we conclude that this single test confirms the Copernican principle and rules out the adiabatic void model as a viable alternative to dark energy.
It is also possible to test the stronger version of the
Copernican principle, which argues that there is no special region in the universe. Such special regions, if exist, are generically associated with “abnormal” motions against
CMB, therefore the kSZ test also applies to these cases. The key obstacle to apply such test for this strong Copernican principle is to isolate such regions in the CMB sky. The kSZ tomography technique proposed by Zhang (2010), through the aid of galaxy redshift surveys, is in principle able to overcome this problem.
General relativity has been confirmed to great accuracy in solar system and binary star systems. However, although a variety of probes can be used to test gravity at galactic scales and above (Jain and Zhang, 2008), test accuracies are in general orders of magnitude worse (Jain & Khoury,
2010). Hence the possibility remains that gravity needs to be modified at these scales. Some of these modifications lead to late time cosmic acceleration (Clifton et al ., 2011) and are topics of active discussions.
There are many obstacles to the test of general relativity at cosmological scales. They can be classified as follows: (1) Uncertainties in initial conditions of the observable universe. One example regards to the
Copernican principle. As we discussed in the previous section, the observed dimming in type Ia supernovae implies cosmic acceleration and would lead to either the introduction of dark energy or the modification of gravity.
However, it could also be just a mirage of the failure of a fundamental principle, the Copernican principle. (2)
Uncertainties in fundamental principles and uncertainties in treating the nonlinear gravitational evolution. The field equation of general relativity is nonlinear in metric. This causes the long-standing backreaction problem, a topic of intensive recent discussion. Other examples include dark matter-dark energy-curvature degeneracy, dark energymodified gravity degeneracy and degeneracies within dark energy paradigm or within modified gravity paradigm. (3)
Uncertainties in treating complicated gastrophysics. One well-known example is the galaxy bias. (4) Uncertainties in measurements. All cosmological probes more or less have this kind of problems (Refer to Dark energy task force report, Albrecht et al ., 2006). Dealing with these measurement biases is a crucial issue in precision cosmology and it can be dauntingly challenging.
There are intensive and active efforts to understand and overcome these issues. In 2007, we proposed an E
G
method to test gravity at cosmological scales (Zhang et al.
, 2007). E
G
is essentially the ratio of two measurements. One is the galaxygalaxy lensing and the other is the galaxy-velocity cross correlation. It is effective in reducing the above uncertainties.
(1) By taking the ratio, the E
G
estimator eliminates uncertainties in the initial fluctuations of the universe. (2) It also eliminates the galaxy bias. (3) E
G
is essentially a test of the Poisson equation at a cosmological scale, so it is sensitive to the nature of gravity and is less affected by degeneracy in modified gravity models or dark energy-modified gravity degeneracy. (4)
In principle, E
G
can be measured to an accuracy of the order of one percent by stage IV dark energy project and is hence able to test general relativity at cosmological scales with such an accuracy. Fig. 2 shows our forecast on future E
G
measurements and its promising power to discriminate between competing gravity models.
The first E
G
measurement was successfully performed by Reyes et al.
(2010). Through the lensing and redshift distortion of luminous red galaxies in Sloan digital sky survey, they managed to measure E
G
at O (10
Mpc) scales and found E
G
=0.39±0.06 at redshift z=0.3.
This measurement is consistent with the prediction of
Fig.2 E
G
as a smoking gun of gravity. Error estimation is based on the standard LCDM and error bars are centered on the LCDM prediction (black solid straight line). The horizontal axis is inverse of scales. Curves are predictions of competing modified gravity models.
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standard LCDM cosmology based on general relativity with a non-zero cosmological constant. Although with the current accuracy it can not distinguish between general relativity and f(R) gravity, it disfavors TeVeS, a relativistic version of MOND. This work confirms the feasibility of the E
G
measurement and demonstrates its great promise as a powerful probe of gravity. We expect significant improvements in E
G
from the ongoing stage
III projects and the planned stage IV projects. Meanwhile modeling of the redshift distortion needs to be improved in order to match the power of these projects (Okumaru
& Jing, 2011).
Great advances in cosmological observations open precious windows to test foundations of modern cosmology, from the origin of the universe to the nature of gravity. We have shown tests against the Copernican principle and general relativity at cosmological scales as examples. Our works, along with others, have robustly ruled out the possibility that we live in a gigantic Gpc size void. These works confirm the Copernican principle and consolidate the existence of late time cosmic acceleration and hence dark energy/ modified gravity. Test of general relativity at cosmological scales is often complicated by unknown galaxy bias and unknown initial fluctuations. The E
G
method proposed by us circumvents these problems and has been applied to existing surveys to confirm general relativity at tens of Mpc scale.
References
Albrecht, A. et al . 2006, Report of the Dark Energy Task Force,
arXiv:astro-ph/0609591.
Clifton, T. et al . 2011, Modified Gravity and Cosmology. eprint
arXiv:1106.2476.
Dunkley, J. et al . 2010, The Atacama Cosmology Telescope:
Cosmological Parameters from the 2008 Power Spectra. eprint
arXiv:1009.0866.
Jain, B. & Khoury, J. 2010, Cosmological Tests of Gravity. Annals of
Physics , Volume 325, Issue 7, p. 1479 1516.
Jain, B. & Zhang, P. 2008, Observational Tests of Modified Gravity.
Physical Review D , vol. 78, Issue 6, id. 063503.
Okumura, T. & Jing, Y. 2011, Systematic Effects on Determination of
the Growth Factor from Redshift-space Distortions. The Astrophysical
Journal , Volume 726, Issue 1, article id. 5.
Reyes, R. et al . 2010, Confirmation of General Relativity on Large
Scales from Weak Lensing and Galaxy Velocities. Nature , Volume
464, Issue 7286, pp. 256 258.
Shirokoff, E. et al . 2010, Improved Constraints on Cosmic Microwave
Background Secondary Anisotropies from the Complete 2008 South
Pole Telescope Data. eprint arXiv:1012.4788
Zhang, P. et al . 2007, Probing Gravity at Cosmological Scales by
Measurements Which Test the Relationship between Gravitational
Lensing and Matter Overdensity. Physical Review Letters , 99,
141302.
Zhang, P. 2010, The Dark Flow Induced Small-scale Kinetic Sunyaev-
Zel'dovich Effect. Monthly Notices of the Royal Astronomical Society:
Letters , Volume 407, Issue 1, pp. L363 L40.
Zhang, P. & Stebbins, A. 2011, Confirmation of the Copernican Principle
at Gpc Radial Scale and Above from the Kinetic Sunyaev Zel'dovich
Effect Power Spectrum. Physical Review Letters , 107, 041301.
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