Lensed Cosmic Microwave Background Constraints on Post-General Relativity Parameters

📝 Abstract

The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parameterized as $1 +\varpi_0 (1 + z)^{-S} $, between the gravitational potentials conventionally appearing in the geodesic equation and the Poisson equation. Current CMB data indicate $\varpi_0=1.67^{+3.07}_{-1.87}$ at the 2 $\sigma$ confidence level, while $S$ remains unconstrained. The departure from GR affects the lensing conversion of E-mode into B-mode polarization. Hence, the lensing measurements from a future CMBpol experiment should be able to improve the constraints to $\varpi_0< 0.30$ for a fiducial $\varpi_0=0$ model and independent of $S $.

💡 Analysis

The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parameterized as $1 +\varpi_0 (1 + z)^{-S} $, between the gravitational potentials conventionally appearing in the geodesic equation and the Poisson equation. Current CMB data indicate $\varpi_0=1.67^{+3.07}_{-1.87}$ at the 2 $\sigma$ confidence level, while $S$ remains unconstrained. The departure from GR affects the lensing conversion of E-mode into B-mode polarization. Hence, the lensing measurements from a future CMBpol experiment should be able to improve the constraints to $\varpi_0< 0.30$ for a fiducial $\varpi_0=0$ model and independent of $S $.

📄 Content

arXiv:0901.0917v1 [astro-ph.CO] 7 Jan 2009 Lensed Cosmic Microwave Background Constraints on Post-General Relativity Parameters Paolo Serra1, Asantha Cooray1 Scott F. Daniel2, Robert Caldwell2, Alessandro Melchiorri3 1Center for Cosmology, Department of Physics and Astronomy, University of California, Irvine, CA 92697 2Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 USA and 3Physics Department and Sezione INFN, University of Rome, “La Sapienza,” P.le Aldo Moro 2, 00185 Rome, Italy (Dated: October 28, 2018) The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parameterized as 1 + ̟0(1 + z)−S, between the gravitational potentials conventionally appearing in the geodesic equation and the Poisson equation. Current CMB data indicate ̟0 = 1.67+3.07 −1.87 at the 2σ confidence level, while S remains unconstrained. The departure from GR affects the lensing conversion of E-mode into B-mode polarization. Hence, the lensing measurements from a future CMBpol experiment should be able to improve the constraints to ̟0 < 0.30 for a fiducial ̟0 = 0 model and independent of S. Introduction—The quest for the source of the cosmic acceleration has led to speculation that the proper theory for gravitation departs from general relativity (GR) on cosmological length scales (e.g. Ref. [1]). There are numerous theoretical examples that intro- duce new gravitational degrees of freedom and that are capable of producing a late-time acceleration, with wide-ranging implications for observable phenomena (e.g. Refs. [2, 3]). Given this possible abundance in new physics, it is important to identify tests that can distinguish between the effects of dark energy and those of modified gravity. Though late-time acceler- ated cosmic expansion is the principal indicator that a new “dark” physics is needed, it is not the only test such physics must satisfy. A successful cosmol- ogy must also agree with measurements related to the behavior of inhomogeneities as probed by the cosmic microwave background and large-scale structure. To understand the extent to which cosmological data support GR, we make use of an approach mo- tivated by the post-Newtonian parameterization of the gravitational field within the Solar system and in- troduce a post-GR parameterization for cosmological perturbations. Such a parameterization is also moti- vated by the common feature within a broad range of gravity theories of a decoupling of the perturbed Newtonian-gauge gravitational potentials φ and ψ, de- fined by the perturbed Robertson-Walker line-element ds2 = a2  −(1 + 2ψ) dτ 2 + (1 −2φ) d⃗x2 , (1) using the notation and convention of Ref. [4]. Whereas GR predicts ψ = φ in the presence of non-relativistic matter, a gravitational slip, defined as ψ ̸= φ, occurs in modified gravity theories. For ex- ample, this inequality means that the gravitational potential of a galaxy cluster is not the same poten- tial traced by the geodesic motion of the constituent galaxies. Hence, a new relation between these poten- tials is a launching point for investigations of cosmo- logical manifestations of modified gravity [6, 7]. For primordial cosmological perturbations, the potentials are not completely free, however, as there exists a con- straint equation in the long-wavelength limit [5]. We consider an alternative theory of gravitation that predicts an expansion history indistinguish- able from ΛCDM, accompanied by post-GR effects whereby ψ(τ, ⃗x) = [1 + ̟(τ, x)] × φ(τ, ⃗x), (2) following Refs. [8, 9]. If the new gravitational phe- nomena is to mimic the effects of Λ by changing the amount of spacetime curvature produced by the cos- mic matter density, then we expect ̟ to grow to order unity at late times on large scales. Looking for clues to such a scenario, CMB temperature anisotropies alone provide a weak constraint to ̟ as the departure from GR is primarily manifest in the integrated Sachs- Wolfe effect [10, 11], as illustrated in Fig. 1. However, CMB lensing is also sensitive to ̟ because the lensing deflection of CMB photons by foreground large-scale structure depends on the sum of the potentials ψ + φ [12, 13, 14, 15]. In this Letter, we show that the ex- pected conversion of E-mode to B-mode polarization through lensing [16], shown in Fig. 1, allows a new probe of departures from GR that will be accessible to future CMB B-mode polarization experiments. The lensing of the CMB affects temperature per- turbations at the level of a few percent at arcminute angular scales, which is on the damping tail of CMB anisotropies [17]. Using temperature anisotropy data from WMAP [18] and ACBAR [19] we can only put weak constraints on the post-GR parameterization at present. On the other hand, B-modes at tens of ar- cminute angular scales are mainly due to the lensing conversion from E-modes. Using the combination of E- and B-modes o

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