Holography for Cosmology

We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional QFT. The holographic description correctly reproduces standard inflationary predictions in the limit where a perturbative quantization of fluctuations is justified. In the opposite limit, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large N QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, N and a dimensionful coupling constant, are capable of satisfying the current observational constraints.Comment: 5 pages; new figure displaying predicted spectral running

Observational signatures of holographic models of inflation

We discuss the phenomenology of recently proposed holographic models of inflation, in which the very early universe is non-geometric and is described by a dual three-dimensional quantum field theory (QFT). We analyze models determined by a specific class of dual QFTs and show that they have the following universal properties: (i) they have a nearly scale invariant spectrum of small amplitude primordial fluctuations, (ii) the scalar spectral index runs as alpha_s = -(n_s-1), (iii) the three-point function of primordial scalar perturbations is of exactly the factorizable equilateral form with f_nl^eq=5/36. These properties hold irrespective of the details (e.g. field content, strength of interactions, etc.) of the dual QFT within the class of theories we analyze. The ratio of tensors-to-scalars is determined by the field content of the dual QFT and does not satisfy the slow-roll consistency relations. Observations from the Planck satellite should be able to confirm or exclude these models.Comment: 4 pp, 2 fig

Cosmological 3-point correlators from holography

We investigate the non-Gaussianity of primordial cosmological perturbations using holographic methods. In particular, we derive holographic formulae that relate all cosmological 3-point correlation functions, including both scalar and tensor perturbations, to stress-energy correlation functions of a holographically dual three-dimensional quantum field theory. These results apply to general single scalar inflationary universes that at late times approach either de Sitter spacetime or accelerating power-law cosmologies. We further show that in Einstein gravity all 3-point functions involving tensors can be obtained from correlators containing only positive helicity gravitons, with the ratios of these to the correlators involving one negative helicity graviton being given by universal functions of momenta, irrespectively of the potential of the scalar field. As a by-product of this investigation, we obtain holographic formulae for the full 3-point function of the stress-energy tensor along general holographic RG flows. These results should have applications in a wider holographic context.Comment: 41 page

Holography for inflation using conformal perturbation theory

We provide a precise and quantitative holographic description of a class of inflationary slow-roll models. The dual QFT is a deformation of a three-dimensional CFT by a nearly marginal operator, which, in the models we consider, generates an RG flow to a nearby IR fixed point. These models describe hilltop inflation, where the inflaton rolls from a local maximum of the potential in the infinite past (corresponding to the IR fixed point of the dual QFT) to reach a nearby local minimum in the infinite future (corresponding to the UV of the dual QFT). Through purely holographic means, we compute the spectra and bispectra of scalar and tensor cosmological perturbations. The QFT correlators to which these observables map holographically may be calculated using conformal perturbation theory, even when the dual QFT is strongly coupled. Both the spectra and the bispectra may be expressed this way in terms of CFT correlators that are fixed, up to a few constants, by conformal invariance. The form of slow-roll inflationary correlators is thus determined by the perturbative breaking of the de Sitter isometries away from the fixed point. Setting the constants to their values obtained by AdS/CFT at the fixed point, we find exact agreement with known expressions for the slow-roll power spectra and non-Gaussianities.Comment: 44 pp, 3 fig

Solution of a Braneworld Big Crunch/Big Bang Cosmology

We solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of four-dimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the four-dimensional description fails at the first nontrivial order in (V/c)^2. At this order, there is nontrivial mixing of the two relevant four-dimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly-separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We comment on the cosmological significance of the result and compute other quantities of interest in five-dimensional cosmological scenarios.Comment: 54 pages, 12 figures, URL updated & 3 references adde

Soft limits in holographic cosmology

We study the soft limits of cosmological correlators from a holographic perspective, showing how the inflationary consistency relations arise from the diffeomorphism invariance of the dual quantum field theory. Starting from the corresponding Ward identity, by taking moments we derive the leading and subleading behaviour of the stress tensor 3-point function in the limit as one momentum vanishes. These results are non-perturbative and valid in quantum field theories of a very general nature. Exploiting the known mapping of correlators in the dual quantum field theory to those of the cosmology, we then obtain the leading and subleading soft behaviour of all cosmological 3-point correlators of curvature perturbations and gravitons. Our results thus provide a holographic derivation of all leading and subleading consistency relations for cosmological 3-point functions, and our method is easily generalised. We verify our results explicitly for slow-roll inflation and for strongly coupled holographic cosmologies with a perturbative dual description

Sparse Graph Codes for Quantum Error-Correction

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small: a constant number per quantum bit, independent of the blocklength. Third, sparse graph codes often offer great flexibility with respect to blocklength and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened version was resubmitted to IEEE Transactions on Information Theory Jan 20, 200