Gauge-invariant Analysis Research Articles

Renormalization of the primordial inflationary power spectra

It has been suggested that the effects of renormalization significantly reduce the amplitude of the inflationary spectra at scales measurable in the cosmic microwave background. Via a gauge-invariant analysis, we compute the renormalized scalar and tensor power spectra and follow their evolution in an inflating universe that undergoes a transition to an FRW phase with a growing horizon. For perturbations originating from Minkowski vacuum fluctuations, we show that the standard prediction for the spectra on superhorizon scales is a late-time attractor, while they are UV finite at all times. Our result is independent of the equation of state after inflation, showing that the standard prediction is fully robust.

Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity

Unimodular gravity is one of the oldest geometric gravity theories and alternatives to general relativity. Essentially, it is based on the Einstein–Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that unimodular gravity can be recast as general relativity in the presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at the classical and quantum levels. Here, we present an analysis focused on the classical scalar perturbations around a cosmological background. We focus on the unusual situation in which the typical conservation laws are not adopted. The discussion is extended to the case where a non-minimal coupled scalar field is introduced. We also present a gauge-invariant analysis showing that perturbations in unimodular gravity display instabilities. Our results reinforce that the equivalence is not verified completely at a cosmological perturbative level.

Gauge and scalar fields on CP2 : A gauge-invariant analysis. II. The measure for gauge fields and a 4d WZW theory

We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a hermitian matrix-valued field. There is also a mass-like term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.

Comparing second-order gravitational self-force, numerical relativity, and effective one body waveforms from inspiralling, quasicircular, and nonspinning black hole binaries

We present the first systematic comparison between gravitational waveforms emitted by inspiralling, quasi-circular and nonspinning black hole binaries computed with three different approaches: second-order gravitational self-force (2GSF) theory, as implemented in the 1PAT1 model; numerical relativity (NR), as implemented by the SXS collaboration; and the effective one body (EOB) formalism, as implemented in the TEOBResumS waveform model. To compare the models we use both a standard, time-domain waveform alignment and a gauge-invariant analysis based on the dimensionless function $Q_\omega(\omega)\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. We analyse the domain of validity of the 1PAT1 model, deriving error estimates and showing that the effects of the final transition to plunge, which the model neglects, extend over a significantly larger frequency interval than one might expect. Restricting to the inspiral regime, we find that, while for mass ratios $q = m_1/m_2\le 10$ TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing $\gtrsim 1$rad; conversely, for $q\gtrsim 100$, 1PAT1 is estimated to have phase errors $<0.1$rad on a large frequency interval, while TEOBResumS develops phase differences $\gtrsim1$rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime $15\lesssim q\lesssim 64$, with $<0.5$rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for $q\gtrsim 30$, reducing the dephasing to $\approx0.27$rad even at $q=128$. Our results pave the way for the construction of GSF-informed EOB models for both intermediate and extreme mass ratio inspirals for the next generation of gravitational wave detectors.

Gauge and scalar fields on CP2 : A gauge-invariant analysis. I. The effective action from chiral scalars

A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses, and also on relating the WZW action to the instanton liquid picture of QCD.

Stop-catalyzed baryogenesis beyond the MSSM

Non-minimal supersymmetric models that predict a tree-level Higgs mass above the Minimal Supersymmetric Standard Model (MSSM) bound are well motivated by naturalness considerations. Indirect constraints on the stop sector parameters of such models are significantly relaxed compared to the MSSM; in particular, both stops can have weak-scale masses. We revisit the stop-catalyzed electroweak baryogenesis (EWB) scenario in this context. We find that the LHC measurements of the Higgs boson production and decay rates already rule out the possibility of stop-catalyzed EWB. We also introduce a gauge-invariant analysis framework that may generalize to other scenarios in which interactions outside the gauge sector drive the electroweak phase transition.

Cosmological perturbations in Horava-Lifshitz theory without detailed balance

In the Horava-Lifshitz theory of quantum gravity, two conditions -- detailed balance and projectability -- are usually assumed. The breaking of projectability simplifies the theory, but it leads to serious problems with the theory. The breaking of detailed balance leads to a more complicated form of the theory, but it appears to resolve some of the problems. Sotiriou, Visser and Weinfurtner formulated the most general theory of Horava-Lifshitz type without detailed balance. We compute the linear scalar perturbations of the FRW model in this form of HL theory. We show that the higher-order curvature terms in the action lead to a gravitational effective anisotropic stress on small scales. Specializing to a Minkowski background, we study the spin-0 scalar mode of the graviton, using a gauge-invariant analysis, and find that it is stable in both the infrared and ultraviolet regimes for $0 \le \xi \le 2/3$. However, in this parameter range the scalar mode is a ghost.

Gauge-invariant analysis of perturbations in Chaplygin gas unified models of dark matterand dark energy

We exploit the gauge-invariant formalism to analyse the perturbative behaviourof two cosmological models based on the generalized Chaplygin gas describingboth dark matter and dark energy in the present universe. In the first model weconsider the generalized Chaplygin gas alone, while in the second one we add abaryon component to it. We extend our analysis also into the parameter rangeα>1, where the generalized Chaplygin gas sound velocity can be larger than that of light. In the firstmodel we find that the matter power spectrum is compatible with the observed one only forα<10−5, which makes the generalized Chaplygin gas practically indistinguishable fromΛCDM. In the second model we study the evolution of inhomogeneities of the baryon component. Thetheoretical power spectrum is in good agreement with the observed one for almost all values ofα.However, the growth of inhomogeneities seems to be particularly favoured either for sufficiently smallvalues of α or for . Thus, it appears that the viability of the generalized Chaplygin gas as acosmological model is stronger when its sound velocity is superluminal. Weshow that in this case the generalized Chaplygin gas equation of state canbe changed in an unobservable region in such a way that its equivalentk-essence microscopical model has no problems with causality.

Negative energy and stability in scalar-tensor gravity

Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry negative energy. A gauge-invariant analysis shows that the background Minkowski space is stable at the classical level with respect to linear scalar and tensor inhomogeneous perturbations.

Charged multifluids in general relativity

The exact 1 + 3 covariant dynamical fluid equations for a multi-component plasma, together with Maxwell's equations are presented in such a way as to make them suitable for a gauge-invariant analysis of linear density and velocity perturbations of the Friedmann–Robertson–Walker model. In the case where the matter is described by a two-component plasma where thermal effects are neglected, a mode representing high-frequency plasma oscillations is found in addition to the standard growing and decaying gravitational instability picture. Further applications of these equations are also discussed.

Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

We present a new, fully covariant and manifestly gauge-invariant expression for the temperature anisotropy in the cosmic microwave background radiation resulting from scalar perturbations. We pay particular attention to gauge issues such as the definition of the temperature perturbation and the placing of the last scattering surface. In the instantaneous recombination approximation, the expression may be integrated up to a Rees-Sciama term for arbitrary matter descriptions in flat, open and closed universes. We discuss the interpretation of our result in the baryon-dominated limit using numerical solutions for conditions on the last scattering surface, and confirm that for adiabatic perturbations the dominant contribution to the anisotropy on intermediate scales (the location of the Doppler peaks) may be understood in terms of the spatial inhomogeneity of the radiation temperature in the baryon rest frame. Finally, we show how this term enters the usual Sachs-Wolfe type calculations (it is rarely seen in such analyses) when subtle gauge effects at the last scattering surface are treated correctly.

A gauge-invariant analysis of magnetic fields in general-relativistic cosmology

We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field using the Ellis - Bruni gauge-invariant formalism. The exact nonlinear equations for general-relativistic magnetohydrodynamic evolution are derived. A number of applications are made: the behaviour of small perturbations to Friedmann universes is studied; a comparison is made with earlier Newtonian treatments of cosmological perturbations and some effects of inflationary expansion are examined.

Covariant and gauge-independent perfect-fluid Robertson-Walker perturbations.

In the preceding paper, covariant and gauge-invariant quantities were defined that characterize density inhomogeneities in an almost-uniform model universe in a transparent way. In this paper second-order propagation equations are derived for these quantities in the case of a general "perfect fluid," and their properties examined. We do not use a harmonic decomposition in our definitions, but when such a decomposition is applied, our results are compatible with those obtained by Bardeen in his harmonically based gauge-invariant analysis. Our second-order equation enables a unified and transparent derivation of a series of results in the literature, without any ambiguity from choice of any particular gauge.

Evolution of perturbations in a baryon-dominated universe - Gauge-invariant analysis

view Abstract Citations (43) References (54) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Evolution of Perturbations in a Baryon-dominated Universe: Gauge-invariant Analysis Gouda, Naoteru ; Sasaki, Misao ; Suto, Yasushi Abstract The evolution of scalar (density) perturbations in a baryon-dominated universe is comprehensively studied on the basis of a gauge-invariant method. In particular, the residual anisotropies of the cosmic microwave background radiation are calculated and are compared with the recent observational upper limits. To the extent that the universe has not been reionized after recombination, the observed upper limits of the temperature anisotropies on small angular scales rule out the cosmological models without nonbaryonic dark matter. In turn, this would provide a strong raison d'etre for (nonbaryonic) dark matter, independently of the results of standard primordial nucleosynthesis. Reionization after recombination, if any, might allow an isocurvature baryonic universe as a viable model, only when the initial density power spectrum was very steep. Publication: The Astrophysical Journal Pub Date: June 1989 DOI: 10.1086/167516 Bibcode: 1989ApJ...341..557G Keywords: Baryons; Computational Astrophysics; Gauge Invariance; Perturbation Theory; Relic Radiation; Astronomical Models; Dark Matter; Universe; Astrophysics; COSMIC BACKGROUND RADIATION; COSMOLOGY; EARLY UNIVERSE full text sources ADS |

A general, gauge-invariant analysis of the cosmic microwave anisotropy

view Abstract Citations (147) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A General, Gauge-invariant Analysis of the Cosmic Microwave Anisotropy Abbott, L. F. ; Schaefer, R. K. Abstract A general, gauge-invariant analysis of the large-scale anisotropies in the cosmic background radiation produced by arbitrary scalar, vector, or tensor perturbations in open, closed, or flat Robertson-Walker spacetimes (with no cosmological constant) is presented. The multipole moment predictions for the scale invariant spectrum and Omega = 1 universe predicted by inflationary cosmologies are contrasted with those for other spectra and for open and closed universes. Using the measured value of the dipole moment, limits are set on the expected value of the quadrupole moment as a function of Omega for various spectra. Publication: The Astrophysical Journal Pub Date: September 1986 DOI: 10.1086/164525 Bibcode: 1986ApJ...308..546A Keywords: Background Radiation; Cosmic Rays; Gauge Invariance; Radiation Distribution; Anisotropy; Big Bang Cosmology; Dipole Moments; Microwaves; Normal Density Functions; Space-Time Functions; Space Radiation; COSMIC BACKGROUND RADIATION full text sources ADS |