The so-called <svg style="vertical-align:-2.34499pt;width:30.775px;" id="M2" height="13.6125" version="1.1" viewBox="0 0 30.775 13.6125" width="30.775"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
		<g transform="translate(72,-61.11)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
				<tspan style="font-size: 12.50px; " x="6.9391651" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="11.102664" y="0">𝑅</tspan>
				<tspan style="font-size: 12.50px; " x="20.354883" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>-gravity has recently attracted a lot of interest since it could be, in principle, able to explain the accelerated expansion of the Universe without adding unknown forms of dark energy/dark matter but, more simply, extending the General Relativity by generic functions of the Ricci scalar. However, apart several phenomenological models, there is no final <svg style="vertical-align:-2.34499pt;width:30.775px;" id="M3" height="13.6125" version="1.1" viewBox="0 0 30.775 13.6125" width="30.775"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
		<g transform="translate(72,-61.11)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
				<tspan style="font-size: 12.50px; " x="6.9391651" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="11.102664" y="0">𝑅</tspan>
				<tspan style="font-size: 12.50px; " x="20.354883" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>-theory capable of fitting all the observations and addressing all the issues related to the presence of dark energy and dark matter. An alternative approach could be to &#x201c;reconstruct&#x201d; the form of <svg style="vertical-align:-2.34499pt;width:30.775px;" id="M4" height="13.6125" version="1.1" viewBox="0 0 30.775 13.6125" width="30.775"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
		<g transform="translate(72,-61.11)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
				<tspan style="font-size: 12.50px; " x="6.9391651" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="11.102664" y="0">𝑅</tspan>
				<tspan style="font-size: 12.50px; " x="20.354883" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg> starting from data without imposing particular classes of model. Besides, adopting the same philosophy, we take into
account the possibility that galaxy cluster masses, estimated at X-ray wavelengths, could be explained, without dark matter, reconstructing the weak-field limit of analytic <svg style="vertical-align:-2.34499pt;width:30.775px;" id="M5" height="13.6125" version="1.1" viewBox="0 0 30.775 13.6125" width="30.775"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
		<g transform="translate(72,-61.11)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
				<tspan style="font-size: 12.50px; " x="6.9391651" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="11.102664" y="0">𝑅</tspan>
				<tspan style="font-size: 12.50px; " x="20.354883" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg> models. The
corrected gravitational potential, obtained in this approximation, is used to estimate the total mass of
a sample of 12 well-shaped clusters of galaxies.

Salvatore Capozziello

Vincenzo Salzano

Cosmography and Large Scale Structure by <svg style="vertical-align:-3.56265pt" height="16.6625" version="1.1" viewBox="0 0 33.75 16.6625" width="33.75" 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="x1D453" d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19&#xA;q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" /></g><g transform="matrix(.017,-0,0,-.017,10.976,12.162)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,16.857,12.162)"><path id="x1D445" d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117&#xA;t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" /></g><g transform="matrix(.017,-0,0,-.017,27.804,12.162)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g></svg>-Gravity: New Results

The cosmological constant problem is principally concerned with trying to understand how the zero-point
energy of quantum fields contributes to gravity. Here we take the approach that by addressing a
fundamental unresolved issue in quantum theory, we can gain a better understanding of the problem.
Our starting point is the observation that the notion of classical time is external to quantum mechanics.
Hence there must exist an equivalent reformulation of quantum mechanics which does not refer to an
external classical time. Such a reformulation is a limiting case of a more general quantum theory which
becomes nonlinear on the Planck mass/energy scale. The nonlinearity gives rise to a quantum-classical
duality which maps a &#x0201c;strongly quantum, weakly gravitational&#x0201d; dynamics to a &#x0201c;weakly quantum, strongly
gravitational&#x0201d; dynamics. This duality predicts the existence of a tiny nonzero cosmological constant of
the order of the square of the Hubble constant, which could be a possible source for the observed cosmic
acceleration. Such a nonlinearity could also be responsible for the collapse of the wave function during a
quantum measurement.

T. P. Singh

Quantum Theory, Noncommutative Gravity, and the Cosmological Constant Problem

The only viable alternative to dark matter is one in which Newtonian dynamics
or gravity breaks down in the limit of low accelerations, as in modified Newtonian dynamics (MONDs). This hypothesis, suggested by Milgrom, has been successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter&#x2014;a critical acceleration which is on the order of the cosmologically interesting value of <svg style="vertical-align:-3.2316pt;width:25.887501px;" id="M1" height="14.3625" version="1.1" viewBox="0 0 25.887501 14.3625" width="25.887501"  xmlns="http://www.w3.org/2000/svg">
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			<text transform="matrix(1,0,0,-1,-71.95,63.79)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
				<tspan style="font-size: 12.50px; " x="5.188745" y="0">𝐻</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-55.85,60.66)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
			</text>

		</g>
	</g>
</svg>. MOND may be viewed as an algorithm for calculating the distribution of force in an astronomical object from the observed distribution of baryonic matter. The fact that it works very well on the scale of galaxies is problematic for cold
dark matter (CDM). Here I present evidence in favor of this assertion and claim that this is, in effect, a falsification of CDM on the scale of galaxies.

R. H. Sanders

Modified Newtonian Dynamics: A Falsification of Cold Dark Matter

We discuss recent laboratory experiments with rotating superconductors and show that three so far unexplained experimentally observed effects (anomalous acceleration signals, anomalous gyroscope signals, Cooper pair mass excess) can be physically explained in terms of a possible interaction of dark energy with Cooper pairs. Our approach is based on a Ginzburg-Landau-like model of electromagnetic dark energy, where gravitationally active photons obtain mass in the superconductor. We show that this model can account simultaneously for the anomalous acceleration and anomalous gravitomagnetic fields around rotating superconductors measured by Tajmar et al. and for the anomalous Cooper pair mass in superconductive Niobium, measured by Cabrera and Tate. It is argued that these three different physical effects are ultimately different experimental manifestations of the simultaneous spontaneous breaking of gauge invariance and of the principle of general covariance in superconductive materials.

Clovis Jacinto de Matos

Christian Beck

Possible Measurable Effects of Dark Energy in Rotating Superconductors

We present new analysis of the birth rate of AXPs and SGRS and their associated SNRs. Using
Kolmogorov-Smirnov statistics together with parametric fits based on a robust estimator, we find a birth rate of ~1/(1000 years) for AXPs/SGRs and their associated SNRs. These high rates suggest that all massive stars (greater
than ~(23–32)<svg style="vertical-align:-3.46715pt;width:25.0875px;" id="M1" height="15.4875" version="1.1" viewBox="0 0 25.0875 15.4875" width="25.0875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D440" d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28&#xA;q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" /></g><g transform="matrix(.012,-0,0,-.012,17.412,15.187)"><path id="x2299" d="M573 255q0 -114 -81.5 -194.5t-197.5 -80.5t-197.5 80.5t-81.5 194.5t81.5 194.5t197.5 80.5t197.5 -80.5t81.5 -194.5zM521 255q0 96 -66.5 163.5t-160.5 67.5t-160.5 -67.5t-66.5 -163.5t66.5 -163.5t160.5 -67.5t160.5 67.5t66.5 163.5zM350 255q0 -26 -16 -42&#xA;t-40 -16t-40 16t-16 42q0 25 16 41.5t40 16.5t40 -16.5t16 -41.5z" /></g></svg>) give rise to remnants with magnetar-like fields. Observations indicate a limited fraction of
high magnetic fields in these progenitors; thus our study is suggestive of magnetic field amplification. Dynamo
mechanisms during the birth of the neutron stars require spin rates much faster than either observations or theory
indicate. We propose that massive stars produce neutron stars with normal (~<svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M2" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" /></g></svg> G) magnetic fields, which are
then amplified to <svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M3" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x31" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><use xlink:href="#x30" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x34" d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" /></g></svg>-<svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M4" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x31" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><use xlink:href="#x30" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z" /></g></svg> G after a delay of hundreds of years. The amplification is speculated to be a consequence
of color ferromagnetism and to occur with a delay after the neutron star core reaches quark deconfinement density
(i.e., the quark-nova scenario). The delayed amplification allows one to interpret simultaneously the high birth
rate and high magnetic fields of AXPs/SGRs and their link to massive stars.

Denis Leahy

Rachid Ouyed

SGRs and AXPs: Evidence for Delayed Amplification of Magnetic Field after Neutron Star Formation?

If a quark-nova occurs inside a collapsar, the interaction between the quark-nova ejecta (relativistic iron-rich chunks) and the collapsar envelope leads to features indicative of those observed in Gamma Ray Bursts. The quark-nova ejecta collides with the stellar envelope creating an outward moving cap (<svg style="vertical-align:-0.0pt;width:23.4375px;" id="M1" height="11.175" version="1.1" viewBox="0 0 23.4375 11.175" width="23.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x393" d="M485 501l-30 -4q-15 64 -35 90q-12 16 -33.5 22t-68.5 6h-74q-21 0 -26.5 -5t-5.5 -26v-458q0 -62 15.5 -78t83.5 -20v-28h-270v28q58 4 72 20t14 78v399q0 61 -13.5 77t-71.5 20v28h433q0 -51 10 -149z" /></g><g transform="matrix(.017,-0,0,-.017,13.39,11.113)"><path id="x223C" d="M548 311q-21 -57 -59 -94t-89 -37q-53 0 -128 52q-55 38 -84 38q-39 0 -70.5 -23t-45.5 -60l-32 12q21 57 59 94t89 37q53 0 128 -52q55 -38 84 -38q39 0 70.5 23t45.5 60z" /></g></svg> 1–10) above the polar funnel. Prompt gamma-ray burst emission from internal shocks in relativistic jets (following accretion onto the quark star) becomes visible after the cap becomes optically thin. Model features include (i) precursor activity (optical, X-ray, <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M2" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D6FE" d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5&#xA;t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z" /></g></svg>-ray), (ii) prompt <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M3" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FE" /></g></svg>-ray emission, and (iii) afterglow emission. We discuss SN-less long duration GRBs, short hard GRBs (including association and nonassociation with star forming regions), dark GRBs, the energetic X-ray flares detected in Swift GRBs, and the near-simultaneous optical and <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M4" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FE" /></g></svg>-ray prompt emission observed in GRBs in the context of our model.

Jan Staff

Brian Niebergal

Quark-Nova Explosion inside a Collapsar: Application to Gamma Ray Bursts

we continue our study of the CMB temperature polarization (TE) cross-correlation as a source of
information about primordial gravitational waves (PGWs). In a previous paper, we considered two
methods for detecting PGWs using the TE cross-correlation. The first method is the zero multipole
method, where we find the multipole, <svg style="vertical-align:-3.3907pt;width:13.45px;" id="M1" height="15.5375" version="1.1" viewBox="0 0 13.45 15.5375" width="13.45" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.25)"><path id="x2113" d="M363 114l21 -20q-62 -106 -161 -106q-61 0 -94 40t-33 138v56l-54 -40l-14 27l68 57v89q0 112 15.5 166t49.5 91q43 46 96 46q44 0 71 -32.5t27 -88.5q0 -41 -17.5 -81.5t-49.5 -76t-55.5 -57t-55.5 -46.5v-87q0 -138 81 -138q60 0 105 63zM177 421v-101q117 105 117 217&#xA;q0 38 -15 60.5t-41 22.5q-34 0 -47.5 -46.5t-13.5 -152.5z" /></g><g transform="matrix(.012,-0,0,-.012,7.05,15.325)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g></svg>, where the TE cross-correlation power spectrum, <svg style="vertical-align:-3.3907pt;width:28.174999px;" id="M2" height="20.549999" version="1.1" viewBox="0 0 28.174999 20.549999" width="28.174999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.263)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5&#xA;t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.012,-0,0,-.012,12.05,20.35)"><use xlink:href="#x2113" /></g><g transform="matrix(.012,-0,0,-.012,12.05,8.1)"><path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22&#xA;t37 -4h417q23 0 33.5 5t25.5 21h23z" /></g><g transform="matrix(.012,-0,0,-.012,19.975,8.1)"><path id="x1D438" d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5&#xA;l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" /></g></svg>, first changes sign. The second method Wiener filters the CMB TE data to remove the density
perturbation contribution to the TE power spectrum. We then use statistical tests to determine
if there is a detection of negative residual TE correlation and hence a detection of primordial
gravitational waves, the only source of negative TE correlation at these superhorizon scales. In this
paper, we will apply these tests to the WMAP 5-year data. We find that the TE power spectrum
consistent with <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M3" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g></svg> &lt; 2.0 at 95% confidence with no additional assumptions about the PGWs. If we
assume that the PGWs are generated by inflation, then we get <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M4" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g></svg> &lt; 1.0 at 95% confidence.

N. J. Miller

B. G. Keating

A. G. Polnarev

CMB Temperature Polarization Correlation and Primordial Gravitational Waves: WMAP5

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<p><em>Advances in Astronomy</em> publishes in all areas of astronomy, astrophysics, and cosmology, and accepts observational and theoretical investigations into celestial objects and the wider universe.</p>


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<p>Chief Editor, Professor Trigo-Rodríguez (ICE, IEEC-CSIC), has a background in the formation of primitive solar system minor bodies, the study of their fragments in space and the analysis of their surviving rocks that arrived on the Earth.</p>


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Advances in Astronomy publishes in all areas of astronomy, astrophysics, and cosmology, and accepts observational and theoretical investigations into celestial objects and the wider universe.

Advances in Astronomy