Network Cosmology

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology

The natural science of cosmology

The network of cosmological tests is tight enough now to show that the relativistic Big Bang cosmology is a good approximation to what happened as the universe expanded and cooled through light element production and evolved to the present. I explain why I reach this conclusion, comment on the varieties of philosophies informing searches for a still better cosmology, and offer an example for further study, the curious tendency of some classes of galaxies to behave as island universes.Comment: Keynote lecture at the seventh International Conference on Gravitation and Cosmology, Goa India, December 201

Network cosmology

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology

Cosmological Perturbations in a Universe with a Domain Wall Era

Topologically protected sheet-like surfaces, called domain walls, form when the potential of a field has a discrete symmetry that is spontaneously broken. Since this condition is commonplace in field theory, it is plausible that many of these walls were produced at some point in the early universe. Moreover, for potentials with a rich enough structure, the walls can join and form a (at large scales) homogeneous and isotropic network that dominates the energy density of the universe for some time before decaying. In this thesis, we study the faith of large scale perturbations in a cosmology with a short period of domain wall dominance. Treating the domain wall network as a relativistic elastic solid at large scales, we show that the perturbations that exited the horizon during inflation get suppressed during the domain wall era, before re-entering the horizon. This power suppression occurs because, unlike a fluid-like universe, a solid-like universe can support sizable anisotropic stress gradients across large scales which effectively act as mass for the scalar and tensor modes. Interestingly, the amplitude of the primordial scalar power spectrum can be closer to one in this cosmology and still give the observed value of $10^{-9}$ today. As a result, the usual bounds on the energy scale of inflation get relaxed to values closer to the (more natural) Planck scale. In the last part of this thesis, as an existence proof, we present a hybrid inflation model with $N$ `waterfall' fields that can realize the proposed cosmology. In this model, a domain wall network forms when an approximate $O(N)$ symmetry gets spontaneously broken at the end of inflation, and for $N \geq 5$, we show that there is a region in parameter space where the network dominates the energy density for a few e-folds before decaying and reheating the universe.Comment: Ph.D. Thesis, Dec 201

Wormhole Cosmology and the Horizon Problem

We construct an explicit class of dynamic lorentzian wormholes connecting Friedmann-Robertson-Walker (FRW) spacetimes. These wormholes can allow two-way transmission of signals between spatially separated regions of spacetime and could permit such regions to come into thermal contact. The cosmology of a network of early Universe wormholes is discussed.Comment: 13 pages, in RevTe

Scientific Objectives of Einstein Telescope

The advanced interferometer network will herald a new era in observational astronomy. There is a very strong science case to go beyond the advanced detector network and build detectors that operate in a frequency range from 1 Hz-10 kHz, with sensitivity a factor ten better in amplitude. Such detectors will be able to probe a range of topics in nuclear physics, astronomy, cosmology and fundamental physics, providing insights into many unsolved problems in these areas.Comment: 18 pages, 4 figures, Plenary talk given at Amaldi Meeting, July 201

One vertex spin-foams with the Dipole Cosmology boundary

We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.Comment: 23 pages, 30 figure

Tensor network representations from the geometry of entangled states

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.Comment: 35 pages, 9 figure