In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of the dissertation is devoted to non-linear extensions for the spin-2 case, focusing on unimodular gravity and bigravity. Both theories lead to modifications of General Relativity at large distances and we will study exact solutions, causal structure of those solutions, and perturbation theory (specially for the Lorentz breaking case). Some comments on quantization of these theories can be found in an appendix.
We review an approach developed in the last few years by our group in which GR is modified in the infrared, at an effective level, by nonlocal terms associated to a mass scale. We begin by recalling the notion of quantum effective action and its associated nonlocalities, illustrating some of their features with the anomaly-induced effective actions in $D=2$ and $D=4$. We examine conceptual issues of nonlocal theories such as causality, degrees of freedoms and ghosts, stressing the importance of the fact that these nonlocalities only emerge at the effective level. We discuss a particular class …
We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{μν}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this non-local theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius $r_S$. Rather on the contrary, in the regime $r\ll m^{-1}$ the corrections to the metric generated by a static body in GR are of the form $1+{\…
Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. We then apply this to various infrared gravity models including non-local $Rf(R/ \Box)$ cosmology an…
We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from th…
Here we discuss the ultraviolet and infrared aspects of the noncommutative counterpart of QED, which is called as noncommutative QED, as well as some infrared dynamics of noncommutative Yang-Mills (NCYM) theory. First we demonstrate that the divergence in the theory can be subtracted by the similar counterterms as in ordinary theory at one loop level. Then the anomalous magnetic moment is calculated to see the infrared aspect of the theory which reflects the violation of Lorentz symmetry. The evaluation of the finite part of the photon vacuum polarization shows that the logarithmically singula…
We consider a model with Lorentz-violating vector field condensates, in which dispersion laws of all perturbations, including tensor modes, undergo non-trivial modification in the infrared. The model is free of ghosts and tachyons at high 3-momenta. At low 3-momenta there are ghosts, and at even lower 3-momenta there exist tachyons. Still, with appropriate choice of parameters, the model is phenomenologically acceptable. Beyond a certain large distance scale and even larger time scale, the gravity of a static source changes from that of General Relativity to that of van Dam--Veltman--Zakharov …
Infinite derivative theory of gravity is a modification to the general theory of relativity. Such modification maintains the massless graviton as the only true physical degree of freedom and avoids ghosts. Moreover, this class of modified gravity can address classical singularities. In this thesis some essential aspects of an infinite derivative theory of gravity are studied. Namely, we considered the Hamiltonian formalism, where the true physical degrees of freedom for infinite derivative scalar models and infinite derivative gravity are obtained. Furthermore, the Gibbons-Hawking-York boundar…
We discuss the cosmological consequences of a model based on a non-local infrared modification of Einstein equations. We find that the model generates a dynamical dark energy that can account for the presently observed value of $Ω_{\rm DE}$, without introducing a cosmological constant. Tuning a free mass parameter $m$ to a value $m\simeq 0.67 H_0$ we reproduce the observed value $Ω_{\rm DE}\simeq 0.68$. This leaves us with no free parameter and we then get a pure prediction for the EOS parameter of dark energy. Writing $w_{\rm DE}(a)=w_0+(1-a) w_a$, we find $w_0\simeq-1.04$ and $w_a\simeq -0.0…
We discuss the possible appearance of several rather exotic phenomena in quantum gravity, including UV/IR mixing, novel modifications of infrared phenomenology that extend effective field theory approaches, and the relaxation of the usual notions of locality. We discuss the relevance of such concepts in quantum gravity for quantum information science, cosmology and general quantum gravity phenomenology.
Scalar forces "screened" by the Vainshtein mechanism may hold the key to understanding the cosmological expansion of our universe, while predicting new and exciting features in the interaction between massive bodies. Here we explore the dynamics of the Vainshtein screening mechanism, focusing on the decoupling limit of the DGP braneworld scenario and dRGT massive gravity. We show that there is a vast set of initial conditions whose evolution is well defined and which are driven to the static, screening solutions of these theories. Screening solutions are stable and behave coherently under smal…
We perform a detailed study of the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a non-local term constructed with $m^2g_{μν}\Box^{-1} R$, where $m$ is a mass parameter. The theory generates automatically a dynamical dark energy component, that can reproduce the observed value of the dark energy density without introducing a cosmological constant. Fixing $m$ so to reproduce the observed value $Ω_{\rm DE}\simeq 0.68$, and writing $w(a)=w_0+(1-a) w_a$, the model provides a neat prediction for the equation of state param…
We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation--a background where a scalar field ϕhas a constant velocity, <\dotϕ> = M^2. The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, ρ= -p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical flui…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions are rather general and apply to large class of theories in which, already at the Newtonian level, gravity changes the regime at a certain very large crossover distance $r_c$. In such theories the cosmological evolution gets dramatically modified at the crossover scale, usually exhibiting a "self-accelerated" expansion, which can be differentiated from more c…
Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED. The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field. The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1. Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level. To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated. The dependence on the direction of photon momentum reflects the Lorentz symmetry…
We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term $m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same number of parameters as $Λ$CDM, with $m$ replacing $Ω_Λ$, and is very predictive. At the background level, after fixing $m$ so as to reproduce the observed value of $Ω_M$, we get a pure prediction for the equation of state of dark energy as a function of redshift, $w_{\rm DE}(z)$, with $w_{\rm DE}(0)$ in the range $[-1.165,-1.135]$ as $Ω_M$ varies over the broad range $Ω_M\in [0.20,0.36]$. …
Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $E\approx m$ (or infrared limit). In this limit we show that a $ φ^4$ theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between $ φ^4$ with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also considered and we demonstrate how states of higher energy becomes unstable and spread converting a false vacuum in a true one.
Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well-defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained…
The infrared behavior of propagators and vertices is derived for the maximally Abelian gauge and the Gribov-Zwanziger action relying on functional equations. The derivation and analysis of Dyson-Schwinger equations increase considerably in complexity when going beyond the standard Landau gauge fixing and the available tools have to be improved. For the derivation of the equations a computer program (DoDSE) was developed in order to handle the plethora of terms. The process of determining possible infrared solutions is abstracted to obtain further insight into the structure of the so-called inf…
If the large scale anomalies in the temperature power spectrum of the cosmic microwave background are of primordial origin, they may herald modifications to the slow roll inflationary paradigm on the largest scales. We study the possibility that the origin of the large scale power suppression is a modification of initial conditions during slow roll as a result of a pre-slow roll phase during which the inflaton evolves rapidly. This stage is manifest in a potential in the equations for the Gaussian fluctuations during slow roll and modify the power spectra of scalar perturbations via an initial…
The huge amounts of undetected and exotic dark matter and dark energy needed to make general relativity work on large scales argue that we should investigate modifications of gravity. The only stable, metric-based and invariant alternative to general relativity is $f(R)$ models. These models can explain primordial inflation, but they cannot dispense with either dark matter or dark energy. I advocate nonlocal modifications of gravity, not as new fundamental theories but rather as the gravitational vacuum polarization engendered by infrared quanta produced during primordial inflation. I also dis…
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our discussion around a conception of quantum gravity involving a notion of quantum spacetime that arises in metastring theory. This theory allows for an evolution of a cosmological Universe in which string-dual degrees of freedom decouple as the Universe ages. Importantly such an implementation of quantum gravity allows for the inclusion of a fundamental length sc…
An interpretation of neutrino oscillations based on a modification of relativistic quantum field theory at low energies, without the need to introduce a neutrino mass, is seen to be compatible with all observations.
Two relevant points related to the application of the BFKL formalism to phenomenology are discussed. First, we have presented a set of observables characterizing multi-jet configurations event by event (average transverse momentum, average azimuthal angle, average ratio of jet rapidities) which can be used to find distinct signals of BFKL dynamics at the LHC. A numerical analysis has been shown using the Monte Carlo event generator BFKLex, modified to include higher-order collinear corrections in addition to the transverse-momentum implementation of the NLO kernel. We require to have two tagge…
The quantization of Yang-Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider in particular the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass…
The Newtonian regime of a recent nonlocal extension of general relativity (GR) is investigated. Nonlocality is introduced via a scalar "constitutive" kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of GR. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.
We investigate a modification of the 2+1 dimensional abelian Chern-Simons theory, obtained by adding a Proca mass term to the gauge field. We are particularly interested in the infrared limit, which can be described by two {\it a priori} different "topological" quantum mechanical models. We apply methods of equivariant cohomology and the ensuing supersymmetry to analyze the partition functions of these quantum mechanical models. In particular, we find that a previously discussed phase-space reductive limiting procedure which relates these two models can be seen as a direct consequence of our s…
We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz--Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz-violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to interesting phenomenology.
Motivated by Horava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally acc…
In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis of the infrared asymptotics of propagators in any spatial dimension follows, and a connection to the Landau gauge is given. In the Coulomb gauge Hamiltonian approach, a linearly rising static color Coulomb potential is found, along with an infrared diverging gluon energy, both signaling confinement. The propagators and vertices in the entire momentum regime are calculated with the variational principle.…
We study information-theoretic aspects of the infrared sector of quantum electrodynamics, using the dressed-state approach pioneered by Chung, Kibble, Faddeev-Kulish and others. In this formalism QED has an IR-finite S-matrix describing the scattering of electrons dressed by coherent states of photons. We show that measurements sensitive only to the outgoing electronic degrees of freedom will experience decoherence in the electron momentum basis due to unobservable photons in the dressing. We make some comments on possible refinements of the dressed-state formalism, and how these consideration…
In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar π, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrar…
Perturbative aspects of ultraviolet and infrared dynamics of noncommutative quantum field theory is examined in detail. It is observed that high loop momentum contribution to the nonplanar diagram develops a new infrared singularity with respect to the external momentum. This singular behavior is closely related to that of ultraviolet divergence of planar diagram. It is also shown that such a relation is precise in noncommutative Yang-Mills theory, but the same feature does not persist in noncommutative generalization of QED.
We continue the recent study of the possibility of constructing a consistent infrared modification of gravity by treating the vierbein and connection as independent dynamical fields. We present the generalized Fierz--Pauli equation that governs the propagation of a massive spin-2 mode in a model of this sort in the backgrounds of arbitrary torsionless Einstein manifolds. We show explicitly that the number of propagating degrees of freedom in these backgrounds remains the same as in flat space-time. This generalizes the recent result that the Boulware--Deser phenomenon does not occur in de Sitt…
Soft theorems in gauge theory and gravity encode the universal properties of scattering amplitudes as the zero frequency limit of one or more external states is approached. When the participating particles are treated in the massless limit, the soft theorems are known to depend only on the directions of the states on null infinity. Leveraging this fact, we develop dual two-dimensional descriptions of soft theorems, recasting them as Ward identities of such dual models on the celestial sphere. This is done by first postulating putative holographic representations of the hard scattering amplitud…
We investigate the non-Pauli-Fierz(nPF) theory, a linearized massive gravity with a generic graviton mass term, which has been ignored due to a ghost in its spectrum and the resultant loss of unitarity. We first show that it is possible to use the Lee-Wick mechanism, a unitarization through the decay of a ghost, in order to handle the sixth mode ghost of nPF, and then check for the quantum consistency. Once proven to be consistent, nPF could become a viable candidate for a large distance modification of gravity, because it naturally solves the intrinsic problems that most dark energy/modified …
We discuss a model in which the fundamental scale of gravity is restricted to 10^{-3} eV. An observable modification of gravity occurs simultaneously at the Hubble distance and at around 0.1 mm. These predictions can be tested both by the table-top experiments and by cosmological measurements. The model is formulated as a brane-world theory embedded in a space with two or more infinite-volume extra dimensions. Gravity on the brane reproduces the four-dimensional laws at observable distances but turns to the high-dimensional behavior at larger scales. To determine the crossover distance we smoo…
We show that general infrared modifications of the Einstein-Hilbert action obtained by addition of curvature invariants are not viable. These modifications contain either ghosts or light gravity scalars. A very specific fine-tuning might solve the problem of ghosts, but the resulting theory is still equivalent to a scalar-tensor gravity and thus gives a corrupted picture of gravity at the solar system scale. The only known loophole is that the theory becomes higher dimensional at large distances. The infinite number of degrees of freedom introduced in this way is not reducible to the addition …
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of …
We study a modification of electromagnetism which violates Lorentz invariance at large distances. In this theory, electromagnetic waves are massive, but the static force between charged particles is Coulomb not Yukawa. At very short distances the theory looks just like QED. But for distances larger than 1/m the massive dispersion relation of the waves can be appreciated, and the Coulomb force can be used to communicate faster than the speed of light. In fact, electrical signals are transmitted instantly, but take a time ~ 1/m to build up to full strength. After that, undamped oscillations of t…
It is by now clear that infrared sector of QED has an intriguingly complex structure. Based on earlier pioneering works on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the $U(1)$ charge group of QED to the "Sky" group incorporating the known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality. There it was shown that the "Sky" group is generated by the algebra of angle dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous bre…
The Lee-Nauenberg theorem is a fundamental quantum mechanical result which provides the standard theoretical response to the problem of collinear and infrared divergences. Its argument, that the divergences due to massless charged particles can be removed by summing over degenerate states, has been successfully applied to systems with final state degeneracies such as LEP processes. If there are massless particles in both the initial and final states, as will be the case at the LHC, the theorem requires the incorporation of disconnected diagrams which produce connected interference effects at t…
