DSR as an explanation of cosmological structure

Deformed special relativity (DSR) is one of the possible realizations of a varying speed of light (VSL). It deforms the usual quadratic dispersion relations so that the speed of light becomes energy dependent, with preferred frames avoided by postulating a non-linear representation of the Lorentz group. The theory may be used to induce a varying speed of sound capable of generating (near) scale-invariant density fluctuations, as discussed in a recent Letter. We identify the non-linear representation of the Lorentz group that leads to scale-invariance, finding a universal result. We also examine the higher order field theory that could be set up to represent it

Rainbow universe

The formalism of rainbow gravity is studied in a cosmological setting. We consider the very early universe which is radiation dominated. A novel treatment in our paper is to look for an ``averaged'' cosmological metric probed by radiation particles themselves. Taking their cosmological evolution into account, we derive the modified Friedmann-Robertson-Walker(FRW) equations which is a generalization of the solution presented by Magueijo and Smolin. Based on this phenomenological cosmological model we argue that the spacetime curvature has an upper bound such that the cosmological singularity is absent. These modified $FRW$ equations can be treated as effective equations in the semi-classical framework of quantum gravity and its analogy with the one recently proposed in loop quantum cosmology is also discussed.Comment: 5 page

Asymptotic Flatness in Rainbow Gravity

A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.Comment: 11 page

Quantum symmetry, the cosmological constant and Planck scale phenomenology

We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional parameter proportional to the Planck mass. Such deformations, called kappa-Poincare algebras, imply modified energy-momentum relations of a type that may be observable in near future experiments. Our argument applies in both 2+1 and 3+1 dimensions and assumes only 1) that the low energy limit of a quantum theory of gravity must involve also a limit in which the cosmological constant is taken very small with respect to the Planck scale and 2) that in 3+1 dimensions the physical energy and momenta of physical elementary particles is related to symmetries of the full quantum gravity theory by appropriate renormalization depending on Lambda l^2_{Planck}. The argument makes use of the fact that the cosmological constant results in the symmetry algebra of quantum gravity being quantum deformed, as a consequence when the limit \Lambda l^2_{Planck} -> 0 is taken one finds a deformed Poincare invariance. We are also able to isolate what information must be provided by the quantum theory in order to determine which presentation of the kappa-Poincare algebra is relevant for the physical symmetry generators and, hence, the exact form of the modified energy-momentum relations. These arguments imply that Lorentz invariance is modified as in proposals for doubly special relativity, rather than broken, in theories of quantum gravity, so long as those theories behave smoothly in the limit the cosmological constant is taken to be small.Comment: LaTex, 19 page

Bouncing Universes with Varying Constants

We investigate the behaviour of exact closed bouncing Friedmann universes in theories with varying constants. We show that the simplest BSBM varying-alpha theory leads to a bouncing universe. The value of alpha increases monotonically, remaining approximately constant during most of each cycle, but increasing significantly around each bounce. When dissipation is introduced we show that in each new cycle the universe expands for longer and to a larger size. We find a similar effect for closed bouncing universes in Brans-Dicke theory, where $G$ also varies monotonically in time from cycle to cycle. Similar behaviour occurs also in varying speed of light theories

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde

Quantizing speeds with the cosmological constant

Considering the Barrett-Crane spin foam model for quantum gravity with (positive) cosmological constant, we show that speeds must be quantized and we investigate the physical implications of this effect such as the emergence of an effective deformed Poincare symmetry.Comment: 4 pages, revtex4, 3 figure

Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planck-scale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant.Comment: 26 pages

Weakness of accelerator bounds on electron superluminality without a preferred frame

The reference laboratory bounds on superluminality of the electron are obtained from the absence of in-vacuo Cherenkov processes and the determinations of synchrotron radiated power for LEP electrons. It is usually assumed that these analyses establish the validity of a standard special-relativistic description of the electron with accuracy of at least a few parts in $10^{14}$, and in particular this is used to exclude electron superluminality with such an accuracy. We observe that these bounds rely crucially on the availability of a preferred frame. In-vacuo-Cherenkov processes are automatically forbidden in any theory with "deformed Lorentz symmetry", relativistic theories that, while different from Special Relativity, preserve the relativity of inertial frames. Determinations of the synchrotron radiated power can be used to constrain the possibility of Lorentz-symmetry deformation, but provide rather weak bounds, which in particular for electron superluminality we establish to afford us no more constraining power than for an accuracy of a few parts in $10^4$. We argue that this observation can have only a limited role in the ongoing effort of analysis of the anomaly tentatively reported by the OPERA collaboration, but we stress that it could provide a valuable case study for assessing the limitations of "indirect" tests of fundamental laws of physics.Comment: LaTex, 6 page

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge new, non -- trivial solution to the representation problem. This solution exists 1. for any target space dimension, 2. for Minkowski signature of the target space, 3. without tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies (zero central charge), 7. while preserving manifest target space Poincar\'e invariance and 8. without picking up UV divergences. The existence of this stable solution is exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. Moreover, these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure