Cosmography: Cosmology without the Einstein equations

How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much "dark energy", "dark matter", "quintessence", and/or "phantom matter" is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as "cosmography", and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.Comment: 7 pages; uses iopart.cls setstack.sty. Based on a talk presented at ACRGR4, the 4th Australasian Conference on General Relativity and Gravitation, Monash University, Melbourne, January 2004. To appear in the proceedings, in General Relativity and Gravitatio

Second-order corrections to slow-roll inflation in the brane cosmology

We calculate the power spectrum, spectral index, and running spectral index for the RS-II brane inflation in the high-energy regime using the slow-roll expansion. There exist several modifications. As an example, we take the power-law inflation by choosing an inverse power-law potential. When comparing these with those arisen in the standard inflation, we find that the power spectrum is enhanced and the spectral index is suppressed, while the running spectral index becomes zero as in the standard inflation. However, since second-order corrections are rather small, these could not play a role of distinguishing between standard and brane inflations.Comment: 6 page

Observational Consequences of a Landscape

In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the "overshoot" problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.Comment: 21 pages, 4 figures v2: references adde

Scale of Homogeneity of the Universe from WMAP

We review the physics of the Grishchuck-Zel'dovich effect which describes the impact of large amplitude, super-horizon gravitational field fluctuations on the Cosmic Microwave Background anisotropy power spectrum. Using the latest determination of the spectrum by WMAP, we infer a lower limit on the present length-scale of such fluctuations of 3927 times the cosmological particle horizon (at the 95% confidence level).Comment: 3 pages, 1 figure. Submitted to Phys. Rev. D. Brief Repor

Low scale gravity as the source of neutrino masses?

We address the question whether low-scale gravity alone can generate the neutrino mass matrix needed to accommodate the observed phenomenology. In low-scale gravity the neutrino mass matrix in the flavor basis is characterized by one parameter (the gravity scale M_X) and by an exact or approximate flavor blindness (namely, all elements of the mass matrix are of comparable size). Neutrino masses and mixings are consistent with the observational data for certain values of the matrix elements, but only when the spectrum of mass is inverted or degenerate. For the latter type of spectra the parameter M_{ee} probed in double beta experiments and the mass parameter probed by cosmology are close to existing upper limits.Comment: 10 pages, 1 figur

Constraining slow-roll inflation with WMAP and 2dF

We constrain slow-roll inflationary models using the recent WMAP data combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the slow-roll parameters to be $0 < \epsilon_1 < 0.032$ and $\epsilon_2 + 5.0 \epsilon_1 = 0.036 \pm 0.025$. For inflation models $V \propto \phi^{\alpha}$ we find that $\alpha< 3.9, 4.3$ at the 2$\sigma$ and $3\sigma$ levels, indicating that the $\lambda\phi^4$ model is under very strong pressure from observations. We define a convergence criterion to judge the necessity of introducing further power spectrum parameters such as the spectral index and running of the spectral index. This criterion is typically violated by models with large negative running that fit the data, indicating that the running cannot be reliably measured with present data.Comment: 8 pages RevTeX4 file with six figures incorporate

Second-order corrections to noncommutative spacetime inflation

We investigate how the uncertainty of noncommutative spacetime affects on inflation. For this purpose, the noncommutative parameter $\mu_0$ is taken to be a zeroth order slow-roll parameter. We calculate the noncommutative power spectrum up to second order using the slow-roll expansion. We find corrections arisen from a change of the pivot scale and the presence of a variable noncommutative parameter, when comparing with the commutative power spectrum. The power-law inflation is chosen to obtain explicit forms for the power spectrum, spectral index, and running spectral index. In cases of the power spectrum and spectral index, the noncommutative effect of higher-order corrections compensates for a loss of higher-order corrections in the commutative case. However, for the running spectral index, all higher-order corrections to the commutative case always provide negative spectral indexes, which could explain the recent WMAP data.Comment: 15 pages, no figure, version published in PR

Correlated Hybrid Fluctuations from Inflation with Thermal Dissipation

We investigate the primordial scalar perturbations in the thermal dissipative inflation where the radiation component (thermal bath) persists and the density fluctuations are thermally originated. The perturbation generated in this model is hybrid, i.e. it consists of both adiabatic and isocurvature components. We calculate the fractional power ratio ($S$) and the correlation coefficient ($\cos\Delta$) between the adiabatic and the isocurvature perturbations at the commencing of the radiation regime. Since the adiabatic/isocurvature decomposition of hybrid perturbations generally is gauge-dependent at super-horizon scales when there is substantial energy exchange between the inflaton and the thermal bath, we carefully perform a proper decomposition of the perturbations. We find that the adiabatic and the isocurvature perturbations are correlated, even though the fluctuations of the radiation component is considered uncorrelated with that of the inflaton. We also show that both $S$ and $\cos \Delta$ depend mainly on the ratio between the dissipation coefficient $\Gamma$ and the Hubble parameter $H$ during inflation. The correlation is positive ($\cos\Delta > 0$) for strong dissipation cases where $\Gamma/H >0.2$, and is negative for weak dissipation instances where $\Gamma/H <0.2$. Moreover, $S$ and $\cos \Delta$ in this model are not independent of each other. The predicted relation between $S$ and $\cos\Delta$ is consistent with the WMAP observation. Other testable predictions are also discussed.Comment: 18 pages using revtex4, accepted for publication in PR

What Can WMAP Tell Us About The Very Early Universe? New Physics as an Explanation of Suppressed Large Scale Power and Running Spectral Index

The Wilkinson Microwave Anisotropy Probe microwave background data may be giving us clues about new physics at the transition from a ``stringy'' epoch of the universe to the standard Friedmann Robertson Walker description. Deviations on large angular scales of the data, as compared to theoretical expectations, as well as running of the spectral index of density perturbations, can be explained by new physics whose scale is set by the height of an inflationary potential. As examples of possible signatures for this new physics, we study the cosmic microwave background spectrum for two string inspired models: 1) modifications to the Friedmann equations and 2) velocity dependent potentials. The suppression of low ``l'' modes in the microwave background data arises due to the new physics. In addition, the spectral index is red (n<1) on small scales and blue (n>1) on large scales, in agreement with data.Comment: 18 pages, 2 figures, submitted for publication in Physical Review D, references added in this versio

Large-scale power in the CMB and new physics: An analysis using Bayesian model comparison

Published versio