We study the approach to scaling in axion string networks in the radiation era, through measuring the root-mean-square velocity $v$ as well as the scaled mean string separation $x$. We find good evidence for a fixed point in the phase-space analysis
in the variables $(x,v)$, providing a strong indication that standard scaling is taking place. We show that the approach to scaling can be well described by a two parameter velocity-one-scale (VOS) model, and show that the values of the parameters are insensitive to the initial state of the network. The string length has also been commonly expressed in terms of a dimensionless string length density $zeta$, proportional to the number of Hubble lengths of string per Hubble volume. In simulations with initial conditions far from the fixed point $zeta$ is still evolving after half a light-crossing time, which has been interpreted in the literature as a long-term logarithmic growth. We show that all our simulations, even those starting far from the fixed point, are accounted for by a VOS model with an asymptote of $zeta_*=1.20pm0.09$ (calculated from the string length in the cosmic rest frame) and $v_* = 0.609pm 0.014$.
We investigate first order phase transitions in a holographic setting of five-dimensional Einstein gravity coupled to a scalar field, constructing phase diagrams of the dual field theory at finite temperature. We scan over the two-dimensional paramet
er space of a simple bottom-up model and map out important quantities for the phase transition: the region where first order phase transitions take place; the latent heat, the transition strength parameter $alpha$, and the stiffness. We find that $alpha$ is generically in the range 0.1 to 0.3, and is strongly correlated with the stiffness (the square of the sound speed in a barotropic fluid). Using the LISA Cosmology Working Group gravitational wave power spectrum model corrected for kinetic energy suppression at large $alpha$ and non-conformal stiffness, we outline the observational prospects at the future space-based detectors LISA and TianQin. A TeV-scale hidden sector with a phase transition described by the model could be observable at both detectors.
We present results from the first simulations of networks of Type I Abelian Higgs cosmic strings to include both matter and radiation eras and Cosmic Microwave Background (CMB) constraints. In Type I strings, the string tension is a slowly decreasing
function of the ratio of the scalar and gauge mass-squared, $beta$. We find that the mean string separation shows no dependence on $beta$, and that the energy-momentum tensor correlators decrease approximately in proportion to the square of the string tension, with additional O(1) correction factors which asymptote to constants below $beta lesssim 0.01$. Strings in models with low self-couplings can therefore satisfy current CMB bounds at higher symmetry-breaking scales. This is particularly relevant for models where the gauge symmetry is broken in a supersymmetric flat direction, for which the effective self-coupling can be extremely small. If our results can be extrapolated to $beta simeq 10^{-15}$, even strings formed at $10^{16}$ GeV (approximately the grand unification scale in supersymmetric extensions of the Standard Model) can be compatible with CMB constraints.
Models of symmetry breaking in the early universe can produce networks of cosmic strings threading t Hooft-Polyakov monopoles. In certain cases there is a larger global symmetry group and the monopoles split into so-called semipoles. These networks a
re all known as cosmic necklaces. We carry out large-scale field theory simulations of the simplest model containing these objects, confirming that the energy density of networks of cosmic necklaces approaches scaling, i.e. that it remains a constant fraction of the background energy density. The number of monopoles per unit comoving string length is constant, meaning that the density fraction of monopoles decreases with time. Where the necklaces carry semipoles rather than monopoles, we perform the first simulations large enough to demonstrate that they also maintain a constant number per unit comoving string length. We also compare our results to a number of analytical models of cosmic necklaces, finding that none explains our results. We put forward evidence that annihilation of poles on the strings is controlled by a diffusive process, a possibility not considered before. The observational constraints derived in our previous work for necklaces with monopoles can now be safely applied to those with semipoles as well.
We investigate cosmic string networks in the Abelian Higgs model using data from a campaign of large-scale numerical simulations on lattices of up to $4096^3$ grid points. We observe scaling or self-similarity of the networks over a wide range of sca
les, and estimate the asymptotic values of the mean string separation in horizon length units $dot{xi}$ and of the mean square string velocity $bar v^2$ in the continuum and large time limits. The scaling occurs because the strings lose energy into classical radiation of the scalar and gauge fields of the Abelian Higgs model. We quantify the energy loss with a dimensionless radiative efficiency parameter, and show that it does not vary significantly with lattice spacing or string separation. This implies that the radiative energy loss underlying the scaling behaviour is not a lattice artefact, and justifies the extrapolation of measured network properties to large times for computations of cosmological perturbations. We also show that the core growth method, which increases the defect core width with time to extend the dynamic range of simulations, does not introduce significant systematic error. We compare $dot{xi}$ and $bar v^2$ to values measured in simulations using the Nambu-Goto approximation, finding that the latter underestimate the mean string separation by about 25%, and overestimate $bar v^2$ by about 10%. The scaling of the string separation implies that string loops decay by the emission of massive radiation within a Hubble time in field theory simulations, in contrast to the Nambu-Goto scenario which neglects this energy loss mechanism. String loops surviving for only one Hubble time emit much less gravitational radiation than in the Nambu-Goto scenario, and are consequently subject to much weaker gravitational wave constraints on their tension.
First order phase transitions in the early Universe generate gravitational waves, which may be observable in future space-based gravitational wave observatiories, e.g. the European eLISA satellite constellation. The gravitational waves provide an unp
recedented direct view of the Universe at the time of their creation. We study the generation of the gravitational waves during a first order phase transition using large-scale simulations of a model consisting of relativistic fluid and an order parameter field. We observe that the dominant source of gravitational waves is the sound generated by the transition, resulting in considerably stronger radiation than earlier calculations have indicated.
We explore the cosmological dynamics of an effective f(R) model constructed from a renormalisation group (RG) improvement of the Einstein--Hilbert action, using the non-perturbative beta functions of the exact renormalisation group equation. The resu
lting f(R) model has some remarkable properties. It naturally exhibits an unstable de Sitter era in the ultraviolet (UV), dynamically connected to a stable de Sitter era in the IR, via a period of radiation and matter domination, thereby describing a non-singular universe. We find that the UV de Sitter point is one of an infinite set, which make the UV RG fixed point inaccessible to classical cosmological evolution. In the vicinity of the fixed point, the model behaves as R^2 gravity, while it correctly recovers General Relativity at solar system scales. In this simplified model, the fluctuations are too large to be the observed ones, and more ingredients in the action are needed.
In cosmological models where local cosmic strings are formed at the end of a period of inflation, the perturbations are seeded both by the defects and by the quantum fluctuations. In a subset of these models, for example those based on $D$-term infla
tion, the amplitudes are similar. Using our recent calculations of structure formation with cosmic strings, we point out that in a flat cosmology with zero cosmological constant and 5% baryonic component, strings plus inflation fits the observational data much better than each component individually. The large-angle CMB spectrum is mildly tilted, for Harrison-Zeldovich inflationary fluctuations. It then rises to a thick Doppler bump, covering $ell=200-600$, modulated by soft secondary undulations. The standard CDM anti-biasing problem is cured, giving place to a slightly biased scenario of galaxy formation.
We compute the power spectra in the cosmic microwave background and cold dark matter (CDM) fluctuations seeded by strings, using the largest string simulations performed so far to evaluate the two-point functions of their stress energy tensor. We fin
d that local strings differ from global defects in that the scalar components of the stress-energy tensor dominate over vector and tensor components. This result has far reaching consequences. We find that cosmic strings exhibit a single Doppler peak of acceptable height at high $ell$. They also seem to have a less severe bias problem than global defects, although the CDM power spectrum in the ``standard cosmology (flat geometry, zero cosmological constant, 5% baryonic component) is the wrong shape to fit large scale structure data.
