We compute the cosmological constant in a scale invariant scalar field theory. The gravitational action is also suitably modified to respect scale invariance. Due to scale invariance the theory does not admit a cosmological constant term. The scale invariance is broken by a recently introduced mechanism called cosmological symmetry breaking. This leads to a nonzero cosmological constant. We compute the one loop corrections to the cosmological constant and show that it is finite.
The collisions of cosmic strings loops and the dynamics of junctions formations in expanding backgrounds are studied. The key parameter controlling the dynamics of junctions formation, the cosmic strings zipping and unzipping is the relative size of the loops compared to the Hubble expansion rate at the time of collision. We study analytically and numerically these processes for large super-horizon size loops, for small sub-horizon size loops as well as for loops with the radii comparable to the Hubble expansion rate at the time of collision.
In supersymmetric theories, cosmic strings produced in the early Universe often have a width of TeV scale, while the tension is much larger. In a scaling regime, an infinite cosmic string releases significant fraction of its energy in the form of string loops. These thick string loops lose their energies efficiently by particle emissions, and hence it may have effects on cosmological observations. We study cosmological implications of string loops with TeV scale width in detail and derive constraints on the tension of the string. Implications on future gravitational wave detectors are also dis…
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated holonomy correction should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
We review a construction of holographic geometries dual to N=4 SYM theory on a Friedmann-Robertson-Walker background and in the presence or absence of a gluon condensate and instanton density. We find the most general solution with arbitrary scale factor and show that it is diffeomorphic to topological black holes. We introduce a time-dependent boundary cosmological constant λ(t) and show energy-momentum conservation in this background. For constant λ, the deconfinement properties of the temporal Wilson loop are analysed. In most cases the Wilson loop confines throughout cosmological evolution…
Two independent criteria are presented that together guarantee exponential suppression of the two-loop cosmological constant in non-supersymmetric heterotic strings. They are derived by performing calculations in both the full string theory and in its underlying effective field theory, and come respectively from contributions that involve only physical untwisted states, and contributions that include orbifold twisted states. The criteria depend purely on the spectrum and charges, so a model that satisfies them will do so with no fine-tuning. An additional consistency condition (emerging from t…
We study the one-loop effective action for gravity in a cosmological setup to determine possible cosmological effects of quantum corrections to Einstein theory. By considering the effect of the universal non-local terms in a toy model, we show that they can play an important role in the very early universe. We find that during inflation, the non-local terms are significant, leading to deviations from the standard inflationary expansion.
The incorporation of a small cosmological constant within radiatively-broken scale-invariant models is discussed. We show that phenomenologically consistent scale-invariant models can be constructed which allow a small positive cosmological constant, providing certain relation between the particle masses is satisfied. As a result, the mass of the dilaton is generated at two-loop level. Another interesting consequence is that the electroweak symmetry-breaking vacuum in such models is necessarily a metastable `false' vacuum which, fortunately, is not expected to decay on cosmological time scales…
Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the full theory, addressing the dynamics before the minisuperspace reduction. This mostly preserves the graph structure and SU(2) quantum numbers. In this article, we study the phenomenological consequences of the isotropic sector of the theory, the so-called emergent bouncing universe model. In particular, the parameter space is scanned and we show that the nu…
The existence of a scaling evolution for cosmic string loops in an expanding universe is demonstrated for the first time by means of numerical simulations. In contrast with what is usually assumed, this result does not rely on any gravitational back reaction effect and has been observed for loops as small as a few thousandths the size of the horizon. We give the energy and number densities of expected cosmic string loops in both the radiation and matter eras. Moreover, we quantify previous claims on the influence of the network initial conditions and the formation of numerically unresolved loo…
We propose a mechanism borrowed from string theory which yields a non-singular transition from a phase of Ekpyrotic contraction to the expanding phase of Standard Big Bang cosmology. The same mechanism converts the initial vacuum spectrum of cosmological fluctuations before the bounce into a scale-invariant one, and also changes the spectrum of gravitational waves into an almost scale-invariant one. The scalar and tensor tilts are predicted to be the same, in contrast to the predictions from the "String Gas Cosmology" scenario. The amplitude of the gravitational wave spectrum depends on the ra…
Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge
Institute of Particle and Nuclear Studies, KEK（高能加速器研究机构粒子核研究部）；Department of Particle and Nuclear Physics, SOKENDAI (The Graduate University for Advanced Studies)（高级研究院粒子核物理系）
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A car…
We investigate four-dimensional cosmological vacuum solutions derived from an effective action invariant under global SL(n,R) transformations. We find the general solutions for linear axion field perturbations about homogeneous dilaton-moduli-vacuum solutions for an SL(4,R)-invariant action and find the spectrum of super-horizon perturbations resulting from vacuum fluctuations in a pre big bang scenario. We show that for SL(n,R)-invariant actions with n>3 there exists a regime of parameter space of non-zero measure where all the axion field spectra have positive spectral tilt, as required if l…
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simula…
A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calcula…
The functional formulation and one-loop effective action for scalar self-interacting theory non-linearly coupled with some power of the curvature are studied. After the explicit one-loop renormalization at weak curvature, we investigated numerically the phase structure for such unusual phi^4 theory. It is demonstrated the possibility of curvature-induced phase transitions for positive values of the curvature power, while for negative values the radiative symmetry breaking does not take place. The dynamical mechanism for the explanation of the current smallness of the cosmological constant is p…
The manifestly gauge invariant Exact Renormalisation Group provides a framework for performing continuum computations in SU(N) Yang-Mills theory, without fixing the gauge. We use this formalism to compute the two-loop beta function in a manifestly gauge invariant way, and without specifying the details of the regularisation scheme.
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one characteristic modification expected from loop quantum gravity.
We examine the form of the cosmological constant in the loop expansion of broken maximally supersymmetric supergravity theories, and after embedding, within superstring and M-theory. Supersymmetry breaking at the TeV scale generates values of the cosmological constant that are in agreement with current astrophysical data. The form of perturbative quantum effects in the loop expansion is consistent with this parameter regime.
We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.
The data on a strongly-nonequilibrium superconducting phase transition in the multi-Josephson-junction loop (MJJL), which represents a close analog of one-dimensional Friedmann-Robertson-Walker cosmological model, are used to refine a concentration of topological defects after the phase transitions of Higgs fields in the early Universe. The thermal correlations between the phases of order parameter revealed in MJJL can reduce considerably the expected number of cosmological defects and, thereby, show a new way to resolve the long-standing problem of their excessive concentration.
We derive the gauge invariant perturbation equations for a 5-dimensional bulk spacetime in the presence of a brane. The equations are derived in full generality, without specifying a particular energy content of the bulk or the brane. We do not assume Z_2 symmetry, and show that the degree of freedom associated with brane motion plays a crucial role. Our formalism may also be used in the Z_2 symmetric case where it simplifies considerably.
Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we study how we can get the gauge invariant solution in the sense it satisfies the Ward identity. Properties of the ``gauge-invariant'' solutions are discussed.
We propose a scotogenic model for generating neutrino masses through a three-loop seesaw. It is a minimally extended inert doublet model with a spontaneously broken global symmetry $U(1)'$ and a preserved $\mathbb{Z}_2$ symmetry. The three-loop suppression allows the new particles to have masses at the TeV scale without fine-tuning the Yukawa couplings. The model leads to a rich phenomenology while satisfying all the current constraints imposed by neutrinoless double-beta decay, charged-lepton flavor violation, and electroweak precision observables. The relatively large Yukawa couplings lead t…
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to th…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We derive the all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. All equatio…
A simple algorithm is presented to decompose any 1-loop amplitude for scattering processes of the class 2 fermions -> 4 fermions into a fixed number of gauge-invariant form factors. The structure of the amplitude is simpler than in the conventional approaches and its numerical evaluation is made faster. The algorithm can be efficiently applied also to amplitudes with several thousands of Feynman diagrams.
