Naveen K. Singh

Cosmological Implications of a Scale Invariant Standard Model

We consider a generalization of the standard model of particle physics such that it displays global scale invariance. The gravitational action is also suitably modified to respect this symmetry. This model is interesting since the cosmological constant term is absent in the action. We find that the scale symmetry is broken by the recently introduced cosmological symmetry breaking mechanism. This simultaneously generates all the dimensionful parameters such as Newtons gravitational constant, the particle masses and the vacuum or dark energy. We find that in its simplest version the model predicts the Higgs mass to be very small, which is ruled out experimentally. We consider a further generalization of the model such that it displays local scale invariance. This model was proposed earlier by Cheng. In this case the Higgs particle disappears from the particle spectrum and instead we find a very massive vector boson. Hence the model gives a consistent description of particle physics phenomenology as well as fitting the cosmological dark energy.

Unimodular theory of gravity and inflation

We investigate inflation and its scalar perturbation driven by a massive scalar field in the unimodular theory of gravity. We introduce a parameter ξ with which the theory is invariant under general unimodular coordinate transformations. When the unimodular parameter is , the classical picture of inflation is reproduced in the unimodular theory because it recovers the background equations of the standard theory of general relativity. We show that for , the theory is equivalent to the standard theory of general relativity at the perturbation level. Unimodular gravity constrains the gauge degree of freedom in the scalar perturbation, but the perturbation equations are similar to those in general relativity. For , we derive the power spectrum and the spectral index, and obtain the unimodular correction to the tensor-to-scalar ratio. Depending on the value of ξ, the correction can either raise or lower the value of the tensor-to-scalar ratio.

DARK ENERGY AND DARK MATTER IN GENERAL RELATIVITY WITH LOCAL SCALE INVARIANCE

We consider a generalization of Einsteins general theory of relativity such that it respects local scale invariance. This requires the introduction of a scalar and a vector field in the action. We show that the theory naturally displays both dark energy and dark matter. We solve the resulting equations of motion assuming an FRW metric. The solutions are found to be almost identical to those corresponding to the standard ΛCDM model.

Unimodular Constraint on global scale Invariance

We study a model with global scale invariance within the framework of unimodular gravity. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described [P. D. Mannheim and D. Kazanas, Astrophys. J. 342, 635 (1989)]. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.

CONSTRAINTS ON THE COSMOLOGICAL CONSTANT DUE TO SCALE INVARIANCE

We consider the standard model with local scale invariance. The theory shows exact scale invariance of dimensionally regulated action. We show that massless gauge fields, which may be Abelian or non-Abelian, lead to vanishing contribution to the cosmological constant in this theory. This result follows in the quantum theory, to all orders in the gauge couplings. However, we have not considered contributions higher orders in the gravitational coupling. Similarly we also find that massless fermion fields yield null contribution to the cosmological constant. The effective cosmological constant in this theory is nonzero due to the phenomenon of cosmological symmetry breaking, which also gives masses to all the massive fields, besides generating the Planck mass. We find a simple relationship between the curvature scalar and the vacuum value of the Higgs field in the limit when we ignore all other contributions to the energy density besides the vacuum energy.

Quantum treatment of the Weyl vector meson

The Weyl meson arises in theories with local scale invariance. It acts as a candidate for dark matter in a generalized Standard Model with local scale invariance. The Higgs particle is absent from the physical spectrum in this theory. We consider the quantization of this theory in detail, imposing suitable gauge fixing conditions. We also consider a further generalization of this model which includes an additional real scalar field. In this theory a Higgs like particle remains in the particle spectrum. Since this particle couples to the Weyl meson, it can lead to interesting phenomenology involving this vector field in particle colliders.

Cosmological perturbation analysis in a scale invariant model of gravity

We consider a model for gravity that is invariant under global scale transformations. It includes one extra real scalar field coupled non-minimally to the gravity fields. In this model all the dimensionful parameters such as the gravitational constant and the cosmological constant etc are generated by a solution of the classical equations of motion. Hence, this solution provides a mechanism to break scale invariance. In this paper, we demonstrate the stability of such a solution against small perturbations in a flat FRW background by making a perturbative expansion around this solution and solving the resulting equations linear in the perturbations. This demonstrates the robustness of this symmetry breaking mechanism.

Thermodynamic properties of a magnetically modulated graphene monolayer

The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in the presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their bandwidth oscillates with magnetic field, leading to Weiss-type oscillations in the thermodynamic properties. The effect of magnetic modulation on the thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen oscillations at low and high magnetic fields, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene compared to electrically modulated graphene. On the other hand, the phase remains the same and the amplitude of the oscillation is large when compared with the magnetically modulated two-dimensional electron gas (2DEG). Explicit asymptotic expressions of the density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.

Primordial power spectra of Eddington-inspired Born-Infeld inflation in strong gravity limit

We investigate the scalar and the tensor perturbations of the

Local Scale Invariance and Inflation

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