Can Cosmic Parallax Distinguish Between Anisotrophic Cosmologies?
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University of Pennsylvania ScholarlyCommons Department of Physics Papers Department of Physics 12-11-2009 Can Cosmic Parallax Distinguish Between Anisotrophic Cosmologies? Michele Fontanini University of Pennsylvania, [email protected] Eric J. West University of Pennsylvania, [email protected] Mark Trodden University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/physics_papers Part of the Physics Commons Recommended Citation Fontanini, M., West, E. J., & Trodden, M. (2009). Can Cosmic Parallax Distinguish Between Anisotrophic Cosmologies?. Retrieved from https://repository.upenn.edu/physics_papers/41 Suggested Citation: Fontanini, M., E.J. West and M. Trodden. (2009). "Can cosmic parallax distinguish between anisotropic cosmologies?" Physical Review D. 80, 123515. © 2009 The American Physical Society http://dx.doi.org/10.1103/PhysRevD.80.123515 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/physics_papers/41 For more information, please contact [email protected]. Can Cosmic Parallax Distinguish Between Anisotrophic Cosmologies? Abstract In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax—the relative angular motion of test galaxies over cosmic time. It was recently argued that the nonobservance of this effect in upcoming precision astrometry missions such as GAIA may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: Fontanini, M., E.J. West and M. Trodden. (2009). "Can cosmic parallax distinguish between anisotropic cosmologies?" Physical Review D. 80, 123515. © 2009 The American Physical Society http://dx.doi.org/10.1103/PhysRevD.80.123515 This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/41 PHYSICAL REVIEW D 80, 123515 (2009) Can cosmic parallax distinguish between anisotropic cosmologies? Michele Fontanini,1,2,* Eric J. West,1,2,† and Mark Trodden1,‡ 1Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia Pennsylvania 19104, USA 2Department of Physics, Syracuse University, Syracuse New York 13244, USA (Received 21 September 2009; published 11 December 2009) In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax—the relative angular motion of test galaxies over cosmic time. It was recently argued that the nonobservance of this effect in upcoming precision astrometry missions such as GAIA may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions. DOI: 10.1103/PhysRevD.80.123515 PACS numbers: 98.80.Jk, 98.80.Es due to the void, and on its own violates any strong version I. INTRODUCTION of the Copernican principle, since we must live inside this Homogeneity and isotropy are the cornerstones of the void in order to account for the observed supernovae dim- standard cosmological model, providing not only a tremen- ming. Nevertheless, it has been shown that these models dous simplification of general relativity, but remarkable can provide a satisfactory fit to the luminosity distance- agreement with all observations. Homogeneity is sup- redshift relation of type Ia supernovae and the position of ported by the observed galaxy distribution from large-scale the first peak in the CMB [15,16]. Thus, LTB models have structure surveys, while isotropy is supported by, in par- been suggested as a possible solution to the problem of ticular, the remarkable uniformity of the average tempera- cosmic acceleration, obviating the need for quintessence ture of the cosmic microwave background radiation fields, modifications of gravity, or a cosmological constant, (CMB). Nevertheless, the paradigm-changing observation and considerable effort has been devoted to constraining of cosmic acceleration, now more than a decade old, has them [17–21]. forced cosmologists to reexamine even their most cher- Beyond the usual cosmological tests of homogeneity ished assumptions, including the correctness of general and isotropy, it has recently been suggested that these relativity, a vanishing cosmological constant, and, more models could be further constrained by real time cosmo- recently, homogeneity and isotropy. logical measurements—in particular, precision measure- The primary evidence for the accelerating universe ments of the evolution of the angular positions of distant comes from the unexpected dimming of type Ia supernovae sources. Following the authors of [22], we refer to this [1–8], as measured through their light curves. The connec- effect as cosmic parallax. The expansion of an FRW uni- tion to cosmic acceleration requires the assumptions of verse is isotropic for all observers, and so cosmic parallax homogeneity and isotropy, and thus this raises the possi- would not be observed. Of course although our universe is bility that abandoning one of these principles may allow very close to an FRW universe, it is not exactly so–for for the appearance of accelerated expansion without actual example, on large scales bound structures may acquire acceleration itself. small peculiar velocities, giving rise to a slight deviation Of course, the usual cosmological Friedmann- from observed isotropic expansion. However, to any ob- Robertson-Walker (FRW) metric is so simple by virtue of server living off-center inside the void of an LTB universe, its underlying symmetries. Abandoning these leads to a cosmic evolution itself is anisotropic and is an additional correspondingly more complicated metric. It is convenient source of cosmic parallax. For sufficiently off-center ob- therefore to begin by studying toy models. One class of servers the cosmic parallax due to anisotropic expansion these that has shown some promise in this direction are the would dominate over the contribution from peculiar veloc- Lemaitre-Tolman-Bondi (LTB) metrics, in which we are ities. Cosmic parallax could therefore provide an interest- assumed to live inside a spherically symmetric underdense ing test of void models. Upcoming sky surveys such as region of spacetime (or ‘‘void’’) embedded in an otherwise GAIA [23] may be able to initiate a measurement of this spatially flat and homogeneous Einstein-de Sitter universe effect, requiring only that a similar survey be completed 10 [9–15]. Such a spacetime is manifestly inhomogeneous, years later in order to complete the measurement. The absence of cosmic parallax beyond what is expected *[email protected] from peculiar velocities would put an upper bound on †[email protected] how far our galaxy could be from the center of the void ‡[email protected] in otherwise allowed LTB models. For example, the au- 1550-7998=2009=80(12)=123515(12) 123515-1 Ó 2009 The American Physical Society MICHELE FONTANINI, ERIC J. WEST, AND MARK TRODDEN PHYSICAL REVIEW D 80, 123515 (2009) thors of [22] argue that GAIA may map sufficiently many indicated, by cosmic parallax we mean cosmic parallax quasars, with enough accuracy, so that two such surveys due to anisotropic expansion about an observer. The LTB spaced 10 years apart could detect the additional LTB metric is given by [35–37] contribution to cosmic parallax if the Milky Way is more jR0ðt; rÞj2 than 10 megaparsecs from the center of a 1 Gpc void. If ds2 ¼dt2 þ dr2 þ R2ðt; rÞd 2; (1) after a decade no additional contribution were found, that 1 þ ðrÞ would constrain the Milky Way to lie unnaturally close to where Rðt; rÞ is a position-dependent scale factor, ðrÞ is the center of such a void. related to the curvature of the spatial slices, and ðÞ0 On the other hand, detection of a contribution to the @=@r. The Einstein equations relate Rðt; rÞ to ðrÞ and an cosmic parallax not arising from peculiar velocities would additional arbitrary function of integration ðrÞ. indicate that the expansion of the universe is anisotropic Specifying ðrÞ, ðrÞ, and an initial condition for Rðt; rÞ from our vantage point. In LTB models this would be due completely determines the spacetime. In models with an to living away from the center of the void, and the strength underdense region, or void, surrounded by an overdense of the additional contribution would be related to this region, ðrÞ and ðrÞ roughly correspond to the width of distance. But cosmic parallax not attributable to peculiar the void and the gradient of the boundary between the inner velocities is a generic feature of any cosmological model and outer regions, respectively, and will be specified below. with anisotropic expansion–an observation also made in The LTB metric describes a region of spacetime that is [22]. For example, spacetimes of the Bianchi type would isotropic about the origin but inhomogeneous with respect exhibit an additional contribution to cosmic parallax to the