This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space generated jointly and agreed on by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor we obtained analog Ricci-Jacobi identity and evaluated the gap that occurs at the transition from the original to the image and vice versa, in the case of infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.76004pt" id="M1" height="11.9702pt" version="1.1" viewBox="-0.0498162 -6.21016 19.1657 11.9702" width="19.1657pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-238" d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z"/></g><g transform="matrix(.0095,0,0,-0.0095,7.668,3.264)"><path id="g50-223" d="M558 106L533 129C501 84 476 67 464 67C446 67 435 116 414 239C457 297 508 367 550 440L539 451L484 438C458 390 429 338 404 300H402C375 407 351 451 285 451C168 451 24 312 24 153C24 56 66 -12 132 -12C206 -12 284 64 345 156H347C367 24 386 -12 422 -12C457 -12 503 7 558 106ZM338 206C272 99 215 56 173 56C140 56 116 96 116 170C116 303 194 405 255 405C304 405 324 299 338 206Z"/></g><g transform="matrix(.0095,0,0,-0.0095,12.932,3.264)"><path id="g50-224" d="M563 583C563 664 501 710 433 710C381 710 334 692 285 648C212 582 178 506 149 350L74 -56C49 -190 36 -222 24 -226L30 -257C52 -256 95 -247 121 -229C131 -222 134 -206 165 -21L219 303C254 510 296 665 397 665C447 665 481 626 481 572C481 512 446 457 390 420C367 405 351 400 323 397L302 349C398 338 466 285 466 197C466 117 419 45 306 45C268 45 224 59 198 74L186 50C197 20 228 -14 274 -14C318 -14 359 3 401 26C478 68 554 144 554 225C554 322 493 367 412 396C490 446 563 500 563 583Z"/></g></svg> which is similar to the second fundamental tensor of hypersurfaces <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.04979992pt" id="M2" height="12.1279pt" version="1.1" viewBox="-0.0498162 -12.0781 24.7903 12.1279" width="24.7903pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-90" d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z"/></g><g transform="matrix(.0095,0,0,-0.0095,8.839,-5.984)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g><g transform="matrix(.0095,0,0,-0.0095,13.695,-5.984)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.0095,0,0,-0.0095,19.489,-5.984)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg>, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational).

Nikolay Yaremenko

Derivation of Field Equations in Space with the Geometric Structure Generated by Metric and Torsion

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out to be an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant. Massive fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four-parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating nonsingular scenarios of evolution of the Universe. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerated expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution is a particular limiting case at the lower boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows displaying the main properties of the dark sector analytically. Although the physical nature of dark sector is still unknown, the macroscopic theory can help analyze the role of dark matter in astrophysical phenomena without resorting to artificial model assumptions.

Boris E. Meierovich

Macroscopic Theory of Dark Sector

Neeraj Pant

N. Pradhan

Ksh. Newton Singh

Anisotropic Charged Fluid Sphere in Isotropic Coordinates

We investigate locally rotational symmetric (LRS) Bianchi type I space time  coupled with scalar field. String cosmological models generated by a cloud of strings with particles attached to them are studied in the Brans-Dicke theory. We assume that the expansion scalar is proportional to the shear scalar and also power law ansatz for scalar field. The physical behavior of the resulting model is discussed through different parameters.

R. Venkateswarlu

J. Satish

LRS Bianchi Type-I Inflationary String Cosmological Model in Brans-Dicke Theory of Gravitation

Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach&#x2019;s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.

Hanno Ess&#xe9;n

Gravitational Lagrangians, Mach&#x2019;s Principle, and the Equivalence Principle in an Expanding Universe

We study antigravity, that is, having an effective gravitational constant with a negative sign, in scalar-tensor theories originating from <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.303181pt" id="M2" height="11.9224pt" version="1.1" viewBox="0 -9.61922 26.0984 11.9224" width="26.0984pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-71"></use></g><g transform="matrix(.0135,0,0,-0.0135,8.228,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.0135,0,0,-0.0135,12.916,0)"><use xlink:href="#g113-83"></use></g><g transform="matrix(.0135,0,0,-0.0135,21.411,0)"><use xlink:href="#g113-42"></use></g></svg> theory and in a Brans-Dicke model with cosmological constant. For the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.303181pt" id="M3" height="11.9224pt" version="1.1" viewBox="0 -9.61922 26.0984 11.9224" width="26.0984pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-71"></use></g><g transform="matrix(.0135,0,0,-0.0135,8.228,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.0135,0,0,-0.0135,12.916,0)"><use xlink:href="#g113-83"></use></g><g transform="matrix(.0135,0,0,-0.0135,21.411,0)"><use xlink:href="#g113-42"></use></g></svg> theory case, we obtain the antigravity scalar-tensor theory in the Jordan frame by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we will demonstrate by using a specific <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.303181pt" id="M4" height="11.9224pt" version="1.1" viewBox="0 -9.61922 26.0984 11.9224" width="26.0984pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-71"></use></g><g transform="matrix(.0135,0,0,-0.0135,8.228,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.0135,0,0,-0.0135,12.916,0)"><use xlink:href="#g113-83"></use></g><g transform="matrix(.0135,0,0,-0.0135,21.411,0)"><use xlink:href="#g113-42"></use></g></svg> model, although there is no antigravity in the initial model, it might occur or not in the scalar-tensor counterpart, mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model.

V. K. Oikonomou

N. Karagiannakis

Study of Antigravity in an <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.303181pt" height="11.9224pt" version="1.1" viewBox="0 -9.61922 26.0984 11.9224" width="26.0984pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-71" d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" /><glyph.data ascent="3473" descent="-2876" horiz-adv-x="607" vert-adv-y="607" /></g><g transform="matrix(.0135,0,0,-0.0135,8.228,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" /><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" /></g><g transform="matrix(.0135,0,0,-0.0135,12.916,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" /><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627" /></g><g transform="matrix(.0135,0,0,-0.0135,21.411,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" /><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" /></g></svg> Model and in Brans-Dicke Theory with Cosmological Constant

It is shown that the Einstein gravity and Higgs scalar field have (a) a long-term oscillation phase; (b) cosmological regular solutions with deceleration/acceleration phases. The first has a preceding contracting and subsequent expanding phases and between them there exists an oscillating phase with arbitrary time duration. The behavior of the second solution near to a flex point is in detail considered.

Vladimir Dzhunushaliev

Higgs Field in Universe: Long-Term Oscillation and Deceleration/Acceleration Phases

This paper is devoted to the Hamiltonian analysis of extension of the quasidilaton massive gravity as was proposed recently in
[arXiv:1306.5502]. We show that, for given formulation of the theory, the additional primary constraint that is responsible for the elimination of the Boulware-Deser ghost is missing. We compare this situation with the quasidilaton massive gravity. Finally, we propose the ghost-free extension of quasidilaton massive gravity.

Josef Kluso&#x148;

Consistent Extension of Quasidilaton Massive Gravity

Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this paper, we show how the framework of numerical relativity can be used for studying cosmological models. The author is working to develop a large-scale simulation of the dynamical processes in the early universe. These take into account interactions of dark matter, scalar perturbations, gravitational waves, magnetic fields, and  turbulent plasma. The code described in this report is a GRMHD code based on the Cactus framework and is structured to utilize one of several different differencing methods chosen at run-time. It is being developed and tested on the University of Houston&#x2019;s Maxwell cluster.

David Garrison

Numerical Relativity as a Tool for Studying the Early Universe

By using the partial wave method, we investigate the absorption of massless scalar wave from regular black hole. We numerically carry out the absorption cross section and find that the larger angular momentum quantum number <svg     style="vertical-align:-0.1638pt;width:4.6999998px;" id="M1" height="12.4375" version="1.1" viewBox="0 0 4.6999998 12.4375" width="4.6999998"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D459" d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" /></g>

		
	
</svg> is, the smaller the corresponding maximum value of partial absorption cross section is. Comparing with Schwarzschild case, the absorption cross section of regular black holes is strengthened in both low and high frequency regions, and the absorption cross section oscillates around the geometric optical value in the high frequency region. Generally speaking, the scattering flux is strengthened and its scattering width becomes narrower in the forward direction. There are obvious contrast of scattering properties of different type of regular black hole.

Hai Huang

Ping Liao

Juhua Chen

Yongjiu Wang

Absorption and Scattering Cross Section of Regular Black Holes

The creation of universes in entangled pairs may avoid the initial singularity and it would have observable consequences in a large macroscopic universe like ours, at least in principle. In this paper we describe the creation of an entangled pair of universes from a double instanton, which avoids the initial singularity, in the case of a homogeneous and isotropic universe with a conformally coupled massless scalar field. The thermodynamical properties of interuniversal entanglement might have observable consequences on the properties of our single universe provided that the thermodynamics of entanglement is eventually related to the classical formulation of thermodynamics.

Salvador J. Robles-P&#xe9;rez

Creation of Entangled Universes Avoids the Big Bang Singularity

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (<svg style="vertical-align:-0.23206pt;width:12.4375px;" id="M1" height="11.75" version="1.1" viewBox="0 0 12.4375 11.75" width="12.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path id="x1D43A" d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242&#xA;q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" /></g></svg>) and cosmological constant (<svg style="vertical-align:-0.0pt;width:11.7875px;" id="M2" height="11.425" version="1.1" viewBox="0 0 11.7875 11.425" width="11.7875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path id="x39B" d="M671 0h-247v28q49 7 60 18.5t0 45.5l-155 438h-2q-21 -61 -74 -204.5t-75 -210.5q-15 -51 -4.5 -65t67.5 -22v-28h-221v28q50 9 69 26.5t45 84.5l202 517l32 9l194 -535q23 -61 42 -78.5t67 -23.5v-28z" /></g></svg>). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent <svg style="vertical-align:-0.23206pt;width:12.4375px;" id="M3" height="11.75" version="1.1" viewBox="0 0 12.4375 11.75" width="12.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D43A" /></g></svg> and <svg style="vertical-align:-0.0pt;width:11.7875px;" id="M4" height="11.425" version="1.1" viewBox="0 0 11.7875 11.425" width="11.7875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.363)"><use xlink:href="#x39B" /></g></svg>. A variety of solutions have been found in which <svg style="vertical-align:-0.23206pt;width:12.4375px;" id="M5" height="11.75" version="1.1" viewBox="0 0 12.4375 11.75" width="12.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D43A" /></g></svg> increases and <svg style="vertical-align:-0.0pt;width:11.7875px;" id="M6" height="11.425" version="1.1" viewBox="0 0 11.7875 11.425" width="11.7875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.363)"><use xlink:href="#x39B" /></g></svg> decreases with time <svg style="vertical-align:-0.1638pt;width:5.9250002px;" id="M7" height="10.3875" version="1.1" viewBox="0 0 5.9250002 10.3875" width="5.9250002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,10.125)"><path id="x1D461" d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" /></g></svg>, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

Sanjay Oli

Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

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Journal of Gravity