We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carr
ies EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 pi /e$) of magnetic charge, independent of the electroweak mixing angle $theta_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem is cured by embedding $U(1)_Y$ in a grand unified group such as $SU(5)$. A second composite configuration with only one Nambu monopole and a colored $U(1)_Y$ Dirac monopole that has minimal EM charge of $4pi/e$ is also described. Finally, there exists a configuration with an EM charge of $8pi/e$ as well as screened color magnetic charge.
The NANOGrav collaboration has recently presented its pulsar timing array data which seem compatible with the presence of a stochastic gravity wave background emitted by cosmic strings with a dimensionless string tension $Gmusimeq 2times 10^{-11}-3ti
mes 10^{-10}$ at $95%$ confidence level ($G$ is Newtons constant and $mu$ denotes the string tension). However, there is some tension between these results and the previous pulsar timing array bound $Gmulesssim 4times 10^{-11}$ from the PPTA experiment. We propose a relaxation of this tension by invoking primordial inflation which partially inflates the string network. The latter re-enters the horizon at later times after the end of inflation, and thus the short string loops are not produced. This leads to a reduction of the gravity wave spectrum which is more pronounced at higher frequencies. The reconciliation of the NANOGrav results with the PPTA bound is possible provided that the strings re-enter the horizon at adequately late times. We consider an example of a realistic $SO(10)$ model incorporating successful inflation driven by a gauge singlet real scalar field with a Coleman-Weinberg potential. This model leads to the production of intermediate scale topologically stable cosmic strings that survive inflation. We show regions of the parameter space where the tension between NANOGrav and PPTA is alleviated. Finally, we present an example in which both monopoles and strings survive inflation with the above tension resolved.
We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell (meson) made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spon
taneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2pi/e)$ as well as $Z$-magnetic charge, where $2pi/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $sqrt{3/8}(4pi/e)$, which is in agreement with the Dirac quantization condition. The monopole weighs about 700 GeV, but because of the attached $Z$-magnetic tube it exists, together with the antimonopole, in a magnetic dumbbell configuration whose mass is expected to lie in the TeV range. The presence of these topological structures in $SU(5)$ and $SO(10)$ and in their supersymmetric extensions provides an exciting new avenue for testing these theories in high-energy colliders.
We describe the internal composition of a topologically stable monopole carrying a magnetic charge of $6pi/e$ that arises from the spontaneous breaking of the trinification symmetry $SU(3)_ctimes SU(3)_Ltimes SU(3)_R$ ($G$). Since this monopole carri
es no color magnetic charge, a charge of $6pi/e$ is required by the Dirac quantization condition. The breaking of $G$ to the Standard Model occurs in a number of steps and yields the desired topologically stable monopole (magnetic baryon), consisting of three confined monopoles. The confined monopoles (magnetic quarks) each carry a combination of Coulomb magnetic flux and magnetic flux tubes, and therefore they do not exist as isolated states. We also display a more elaborate configuration (fang necklace) composed of these magnetic quarks. In contrast to the $SU(5)$ monopole which is superheavy and carries a magnetic charge of $2pi/e$ as well as color magnetic charge, the trinification monopole may have mass in the TeV range, in which case it may be accessible at the LHC and its planned upgrades.
We consider magnetic monopoles and strings that appear in non-supersymmetric $SO(10)$ and $E_6$ grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string t
ension parameter $Gmu$ spans the range $10^{-6}-10^{-30}$, where $G$ is Newtons constant and $mu$ is the string tension. We show how intermediate scale monopoles with mass $sim 10^{13}-10^{14}$ GeV and flux $lesssim 2.8times 10^{-16}$ ${mathrm{cm}^{-2}mathrm{s}^{-1}mathrm{sr}^{-1}}$, and cosmic strings with $Gmu sim 10^{-11}-10^{-10}$ survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio $r$ lies between $0.06$ and $0.003$ depending on the details of the inflationary scenario.
We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. A $U(1), R$ symmetry plays an essential role in realizing inflation as well as in eliminating s
ome undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p rightarrow e^{+}(mu^+) + pi^0$, $p rightarrow bar{ u} + pi^{+}$, $p rightarrow K^0 + e^+(mu^{+})$, and $p rightarrow K^+ + bar{ u}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{rm GUT}$ ($sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.
We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $mu$ term arises, following Dvali, Lazarides, and Shafi, from the
coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c times SU(2)_L times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $mu$ coupling, the gravitino mass, and the reheating following inflation is discussed in detail. We explore regions of the parameter space that yield gravitino dark matter and observable gravity waves with the tensor-to-scalar ratio $r sim 10^{-4}-10^{-3}$.
The early stages of the universe evolution are discussed according to the hot big bang model and the grand unified theories. The shortcomings of big bang are summarized and their resolution by inflationary cosmology is sketched. Cosmological inflatio
n, the subsequent oscillation and decay of the inflaton field, and the resulting reheating of the universe are studied in some detail. The density perturbations produced by inflation and the temperature fluctuations of the cosmic microwave background radiation are introduced. Baryogenesis via non-thermal leptogenesis is analyzed and dark energy and matter in the universe are presented. Quantum gravity and string theory are very briefly introduced. The problem of initial conditions for inflation is discussed in the light of string theory and the possibly detectable primordial gravity waves from inflation are mentioned.
We investigate a non-supersymmetric $SO(10)times U(1)_{rm PQ}$ axion model in which the spontaneous breaking of $U(1)_{rm PQ}$ occurs after inflation, and the axion domain wall problem is resolved by employing the Lazarides-Shafi mechanism. This requ
ires the introduction of two fermion 10-plets, such that the surviving discrete symmetry from the explicit $U(1)_{rm PQ}$ breaking by QCD instantons is reduced from $Z_{12}$ to $Z_4$, where $Z_4$ coincides with the center of $SO(10)$ (more precisely $Spin(10)$). An unbroken $Z_2$ subgroup of $Z_4$ yields intermediate scale topologically stable strings, as well as a stable electroweak doublet non-thermal dark matter candidate from the fermion 10-plets with mass comparable to or somewhat smaller than the axion decay constant $f_{rm a}$. We present an explicit realization with inflation taken into account and which also incorporates non-thermal leptogenesis. The fermion dark matter mass lies in the $3times 10^{8}-10^{10}~{rm GeV}$ range and its contribution to the relic dark matter abundance can be comparable to that from the axion.
We show that if global lepton number symmetry is spontaneously broken in a post inflation epoch, then it can lead to the formation of cosmological domain walls. This happens in the well-known Majoron paradigm for neutrino mass generation. We propose
some realistic examples which allow spontaneous lepton number breaking to be safe from such domain walls.
