Cosmic microwave background anisotropies in multiconnected flat spaces

Riazuelo, Alain; Weeks, Jeffrey R.; Uzan, Jean‐Philippe; Lehoucq, Roland; Luminet, Jean‐Pierre

doi:10.1103/physrevd.69.103518

Cited by 81 publications

(157 citation statements)

References 43 publications

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“…Before we proceed, we should clarify that neither this work nor any of those cited depends on the question [75] [76] as to whether a toral spatial structure is directly observable in, for example, the cosmic microwave background. A priori, one does not expect this to be possible, since the size of a flat torus is of course unrelated to its curvature and can be freely prescribed independently of all other parameters.…”

Section: String Gases Topology and The Null Energy Conditionmentioning

confidence: 99%

The phantom divide in string gas cosmology

McInnes

2005

Nuclear Physics B

102

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One of the main virtues of string gas cosmology is that it resolves cosmological singularities. Since the Universe can be approximated by a locally asymptotically de Sitter spacetime by the end of the inflationary era, a singularity theorem implies that these cosmologies effectively violate the Null Energy Condition [not just the Strong Energy Condition]. We stress that this is an extremely robust result, which does not depend on assuming that the spatial sections remain precisely flat in the early Universe. This means, however, that it must be possible for string cosmologies to cross the recently much-discussed phantom divide [from w < −1 to w > −1, where w is the equation-ofstate parameter]. This naturally raises the question as to whether the phantom divide can be crossed again, to account for recent observations suggesting that w < −1 at the present time. We argue that non-perturbative string effects rule out this possibility, even if the NEC violation in question is only "effective".

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Section: String Gases Topology and The Null Energy Conditionmentioning

confidence: 99%

The phantom divide in string gas cosmology

McInnes

2005

Nuclear Physics B

102

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“…In other words, these fluctuations show that multiply connected universes are possible, and the simplest one is a 3-torus [2,3]. Also, simulations of CMB map and the angular power spectrum of temperature fluctuations, considering the torus topology, and comparing them with the observations of the COBE satellite in order to obtain the lower limit of universe size, suggest that we live in a small universe [4][5][6][7][8].…”

Section: Jhep01(2018)017mentioning

confidence: 99%

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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Abstract:We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

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“…4 and 5 respectively. Discussion of spherical, multiply connected spaces is available in Weeks (2001), Gausmann et al (2001), Lehoucq et al (2002), and Riazuelo et al (2004), and we refer the reader to references therein for introductions to cosmic topology. Distances are calculated in a spatial section at constant cosmological time in the universal covering space (S 3 for the spherical spaces, R 3 for T 3 ), by default as "physical" distances, i.e., r = aχ, where a(t) is the scale factor and χ is a comoving distance (i.e.…”

Section: Introductionmentioning

confidence: 99%

The residual gravity acceleration effect in the Poincaré dodecahedral space

Roukema

Różański

2009

A&A

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Context. In a flat space, it has been shown heuristically that the global topology of comoving space can affect the dynamics expected in the weak-field Newtonian limit, inducing a weak acceleration effect similar to dark energy. Aims. Does a similar effect occur in the case of the Poincaré dodecahedral space, which is a candidate model of comoving space for solving the missing fluctuations problem observed in cosmic microwave background all-sky maps? Moreover, does the effect distinguish the Poincaré space from other well-proportioned spaces? Methods. The acceleration effect in the Poincaré space S 3 /I * is studied, using a massive particle and a nearby test particle of negligible mass. Calculations are made in S 3 embedded in R 4 . The weak-limit gravitational attraction on a test particle at distance r is set to be ∝[R C sin(r/R C )] −2 rather than ∝r −2 , where R C is the curvature radius, in order to satisfy Stokes' theorem. A finite particle horizon large enough to include the adjacent topological images of the massive particle is assumed. The regular, flat, 3-torus T 3 is re-examined, and two other well-proportioned spaces, the octahedral space S 3 /T * , and the truncated cube space S 3 /O * , are also studied. Results. The residual gravity effect occurs in all four cases. In a perfectly regular 3-torus of side length L a , and in the octahedral and truncated cube spaces, the highest order term in the residual acceleration is the third-order term in the Taylor expansion in powers of r/L a (3-torus), or r/R C , respectively. However, the Poincaré dodecahedral space is unique among the four spaces. The third order cancels, leaving the fifth order term ∼±300(r/R C ) 5 as the most significant. Conclusions. Not only are three of the four perfectly regular well-proportioned spaces better balanced than most other multiply connected spaces in terms of the residual gravity acceleration effect by a factor of about a million (setting r/L a = r/R C ∼ 10 −3 ), but the fourth of these spaces is about ten thousand times better balanced than the other three. This is the Poincaré dodecahedral space. Is this unique dynamical property of the Poincaré space a clue towards a theory of cosmic topology?

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Cosmic microwave background anisotropies in multiconnected flat spaces

Cited by 81 publications

References 43 publications

The phantom divide in string gas cosmology

The phantom divide in string gas cosmology

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

The residual gravity acceleration effect in the Poincaré dodecahedral space

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