# Lorentz Invariance Breakdown and Constraints from Big-Bang Nucleosynthesis

#### Abstract

Many attempts aimed to construct a quantum theory of gravity have shown that spacetime might have a non trivial topology at the Planck scale. However, the difficulties to build up a complete theory of quantum gravity have motivated the development of semiclassical approaches in which CPT and Lorentz invariance breakdown occur at the level of effective theory. As suggested by Kostelecký and Samuel [1,2], a departure from Lorentz invariance could manifest itself as an effect of non-locality in string theory: The interactions among tensor fields give rise to non-zero expectation values for the Lorentz tensors that induce spontaneously broken Lorentz symmetry. The general effective field theory describing these Lorentz and CPT violations is the Standard Model Extension (SME) [3]. This model, along with the usual SM and gravitational Lagrangian, includes all possible coordinate-invariant terms constructed with SM, gravitational fields, and violating Lorentz symmetry [4]. The aim of this paper is to derive, in the framework of Big-Bang Nucleosynthesis (BBN), bounds on parameters of SME. BBN is a cornerstone of standard cosmology: with cosmic background radiation, it provides a strong evidence that during the early phases i.e. between a fraction of seconds (∼ 0.01 s) and few hundred seconds after the BB the Universe was hot and dense. BBN describes the sequence of nuclear reactions leading to the synthesis of light elements. Our analysis follows the paper by Bernstein, Brown and Feinberg [5], in which the model of helium synthesis in the early Universe is discussed. During the BBN phase, the geometry of the expanding early Universe is described by the Friedman-Robertson-Walker (FRW) metric ds = dt − a(t)(dX + dY 2 + dZ). a(t) is the scale factor (the spatial curvature has been taken equal to zero). The dynamical equation for the evolution of the scale factor is H = 8πG 3 ρ, where H = ȧ/a is the Hubble parameter. The corrections to General Relativity discussed by Kostelecký and Bluhm [4] are not considered here. As shown by Kostelecký and Lehnert [6], the dispersion relation of relativistic fermions is given by

### Cite this paper

@inproceedings{Lambiase2005LorentzIB, title={Lorentz Invariance Breakdown and Constraints from Big-Bang Nucleosynthesis}, author={Gaetano Lambiase}, year={2005} }